unit 1: introduction the

Unit 1: Introduction theScientific Process

Cheryl LewisJean Brainard, Ph.D.Dana Desonie, Ph.D.

Andrew GloagMelissa Kramer

Anne Gloag

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Printed: August 19, 2013

AUTHORSCheryl LewisJean Brainard, Ph.D.Dana Desonie, Ph.D.Andrew GloagMelissa KramerAnne Gloag

EDITORAnnamaria Farbizio

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Contents www.ck12.org

Contents

1 Safety in Science 1

2 Nature of Science 6

3 Scope of Chemistry 22

4 Branches of Earth Science 25

5 International System of Units 29

6 Matter, Mass, Weight, and Volume 40

7 Significant Figures 45

8 Calculating Derived Quantities 51

9 Scientific Graphing 55

10 Scientific Notation 60

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www.ck12.org Chapter 1. Safety in Science

CHAPTER 1 Safety in Science• Identify the meaning of lab safety symbols.• List rules for staying safe in the lab.• State what to do in case of accidents in the lab or field.

Research in science can be exciting, but it also has potential dangers. For example, the field scientist in this photois collecting water samples from a polluted lake. There are many microorganisms in the water that could make hersick. The water and shore are also strewn with dangerous objects such as sharp can lids and broken glass bottles thatcould cause serious injury. Whether in the field or in the lab, knowing how to stay safe in science is important.

Safety Symbols

Lab procedures and equipment may be labeled with safety symbols. These symbols warn of specific hazards, suchas flames or broken glass. Learn the symbols so you will recognize the dangers. Then learn how to avoid them.Many common safety symbols are shown in the Figure 1.1.

Q: Do you know how you can avoid these hazards?

A: Wearing protective gear is one way to avoid many hazards in science. For example, to avoid being burned by hotobjects, use hot mitts to protect your hands. To avoid eye hazards, such as harsh liquids splashed into the eyes, wearsafety goggles. You can learn more about these and other lab hazards and how to avoid them at this URL: http://www.angelfire.com/va3/chemclass/safety.html.

Safety Rules

Following basic safety rules is another important way to stay safe in science. Safe practices help prevent accidents.Several lab safety rules are listed below. Different rules may apply when you work in the field. But in all cases, youshould always follow your teacher’s instructions.

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FIGURE 1.1

Duxbury Public Schools’s uses Flinn Scientific’s Student Safety Contract.

In Case of Accident

Even when you follow the rules, accidents can happen. Immediately alert your teacher if an accident occurs. Reportall accidents, whether or not you think they are serious.

Summary

• Lab safety symbols warn of specific hazards, such as flames or broken glass. Knowing the symbols allowsyou to recognize and avoid the dangers.

• Following basic safety rules, such as wearing safety gear, helps prevent accidents in the lab and in the field.• All accidents should be reported immediately.

Practice

Examine this sketch of students working in a lab, and then answer the question below.

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FIGURE 1.2

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FIGURE 1.3

1. These students are breaking at least six lab safety rules. What are they doing that is unsafe?

Review

1. What hazard do think this safety (Figure 1.4) symbol represents?

FIGURE 1.4Safety symbol.

1. Identify three safety rules that help prevent accidents in the lab.

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2. Create a safety poster to convey one of the three rules you listed in your answer to 2.

References

1. Image copyright Jozsef Szasz-Fabian, 2012. . Used under license from Shutterstock.com2. . . CC BY-NC-SA3. . . CC BY-NC-SA4. Image copyright Fabio Berti, 2012. . Used under license from Shutterstock.com

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CHAPTER 2 Nature of Science

Lesson Objectives

• List the principles that should guide scientific research.• Examine a scientist’s view of the world.• Outline a set of steps that might be used in the scientific method of investigating a problem.• Explain why a control group is used in an experiment.• Outline the role that reasoning plays in examining hypotheses.• Examine the function of the independent variable in an experiment.• Define what is meant by a theory and compare this to the meaning of hypothesis.

Introduction

The goal of science is to learn how nature works by observing the physical world, and to understand it throughresearch and experimentation. Science is a distinctive way of learning about the natural world through observation,inquiry, formulating and testing hypotheses, gathering and analyzing data, and reporting and evaluating findings. Weare all part of an amazing and mysterious phenomenon called "Life" that thousands of scientists everyday are tryingto better explain. And it’s surprisingly easy to become part of this great discovery! All you need is your naturalcuriosity and an understanding of how people use the process of science to learn about the world.

Goals of Science

Science involves objective, logical, and repeatable attempts to understand the principles and forces working in thenatural universe. Science is from the Latin word, scientia, which means “knowledge.” Good science is an ongoingprocess of testing and evaluation. One of the intended benefits for students taking a biology course is that they willbecome more familiar with the scientific process.

Humans are naturally interested in the world we live in. Young children constantly ask "why" questions. Science isa way to get some of those “whys” answered. When we shop for groceries, we are carrying out a kind of scientificexperiment (Figure 2.1). If you like Brand X of salad dressing, and Brand Y is on sale, perhaps you try Brand Y. Ifyou like Y you may buy it again even when it is not on sale. If you did not like Brand Y, then no sale will get you totry it again. To find out why a person makes a particular purchasing choice, you might examine the cost, ingredientlist, or packaging of the two salad dressings.

There are many different areas of science, or scientific disciplines, but all scientific study involves:

• asking questions• making observations• relying on evidence to form conclusions• being skeptical about ideas or results

Skepticism is an attitude of doubt about the truthfulness of claims that lack empirical evidence. Scientific skepti-cism, also referred to as skeptical inquiry, questions claims based on their scientific verifiability rather than acceptingclaims based on faith or anecdotes. Scientific skepticism uses critical thinking to analyze such claims and opposesclaims which lack scientific evidence.

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FIGURE 2.1Shopping sometimes involves a little sci-entific experimentation. You are inter-ested in inventing a new type of salad thatyou can pack for lunch. You might buy avegetable or salad dressing that you havenot eaten before, to discover if you like it.If you like it, you will probably buy it again.That is a type of experiment.

A Scientific View of the World

Science is based on the analysis of things that humans can observe either by themselves through their senses, or byusing special equipment. Science therefore cannot explain anything about the natural world that is beyond what isobservable by current means.

There is no fixed set of steps that scientists always follow and there is no single path that leads to scientificknowledge. There are, however, certain features of science that give it a very specific way of investigating something.You do not have to be a professional scientist to think like a scientist. Everyone, including you, can use certainfeatures of scientific thinking to think critically about issues and situations in everyday life.

Science assumes that the universe is a vast single system in which the basic rules are the same, and thus nature,and what happens in nature, can be understood. Things that are learned from studying one part of the universe canbe applied to other parts of the universe. For example, the same principles of motion and gravitation that explainthe motion of falling objects on Earth also explain the orbit of the planets around the sun, and galaxies, as shown inFigure 2.2. As discussed below, as more and more information and knowledge is collected and understood, scientificideas can change, still scientific knowledge usually stands the test of time (also known as a Law of Nature). Science,however, cannot answer all questions.

FIGURE 2.2With some changes over the years, sim-ilar principles of motion have applied todifferent situations. The same scientificprinciples that help explain planetary or-bits can be applied to the movement of aFerris wheel.

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Nature Can Be Understood

Science presumes that events in the universe happen in patterns that can be understood by careful study. Scientistsbelieve that through the use of the mind, and with the help of instruments that extend the human senses, people candiscover patterns in all of nature that can help us understand the world and the universe.

Scientific Ideas Can Change

Science is a process for developing knowledge. Change in knowledge about the natural world is expected becausenew observations may challenge the existing understanding of nature. No matter how well one theory explains aset of observations, it is possible that another theory may fit just as well or better, or may fit a still wider range ofobservations. In science, the testing and improving of theories goes on all the time. Scientists know that even ifthere is no way to gain complete knowledge about something, an increasingly accurate understanding of nature willdevelop over time.

The ability of scientists to make more accurate predictions about the natural world, from determining how a can-cerous tumor develops a blood supply, to calculating the orbit of an asteroid, provides evidence that scientists aregaining an understanding of how the world works.

Scientific Knowledge Can Stand the Test of Time

Continuity and stability are as much characteristics of science as change is. Although scientists accept someuncertainty as part of nature, most scientific knowledge stands the test of time. A changing of ideas, rather thana complete rejection of the ideas, is the usual practice in science. Powerful ideas about nature tend to survive, growmore accurate and become more widely accepted.

For example, in developing the theory of relativity, Albert Einstein did not throw out Issac Newton’s laws of motionbut rather, he showed them to be only a small part of the bigger, cosmic picture. That is, the Newtonian laws ofmotion have limited use within our more general concept of the universe. For example, the National Aeronauticsand Space Administration (NASA) uses the Newtonian laws of motion to calculate the flight paths of satellites andspace vehicles.

Science Cannot Offer Answers to All Questions

There are many things that cannot be examined in a scientific way. There are, for instance, beliefs that cannot beproved or disproved, such as the existence of supernatural powers, supernatural beings, or the meaning of life. Inother cases, a scientific approach to a question and a scientific answer may be rejected by people who hold to certainbeliefs.

Scientists do not have the means to settle moral questions surrounding good and evil, or love and hate, although theycan sometimes contribute to the discussion of such issues by identifying the likely reasons for certain actions byhumans and the possible consequences of these actions.

Scientific Methods

It can be difficult sometimes to define research methods in a way that will clearly distinguish science from non-science. However, there is a set of core principles that make up the “bones” of scientific research. These principlesare widely accepted within the scientific community and in academia.

We learned earlier in this lesson that there is no fixed set of steps that scientists always follow during an investigation.Similarly, there is no single path that leads scientists to knowledge. There are, however, certain features of sciencethat give it a very specific way of investigating things.

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Scientific investigations examine, gain new knowledge, or build on previous knowledge about phenomena. Aphenomenon, is any occurrence that is observable, such as the burning match shown in Figure 2.3. A phenomenonmay be a feature of matter, energy, or time. For example, Isaac Newton made observations of the phenomenonof the moon’s orbit. Galileo Galilei made observations of phenomena related to swinging pendulums. Althoughprocedures vary from one field of scientific inquiry to another, certain features distinguish scientific inquiry fromother types of knowledge. Scientific methods are based on gathering observable, empirical (produced by experimentor observation), and measurable evidence that is critically evaluated.

FIGURE 2.3The combustion of this match is an observable event and therefore aphenomenon.

A hypothesis is a suggested explanation based on evidence that can be tested by observation or experimentation.Experimenters may test and reject several hypotheses before solving a problem. A hypothesis must be testable; itgains credibility by being tested over and over again, and by surviving several attempts to prove it wrong. Whenwriting a hypothesis for a scientific experiment it is written as an if, then statement. If (this is done), then (this willhappen). Example of a hypothesis : If a ball is thrown up in the air, then it will fall back down.

The Scientific Method Video can be seen at http://www.youtube.com/watch?v=KZaCy5Z87FA&feature=related (3:36).

MEDIAClick image to the left for more content.

Scientific Investigations

The scientific method is not a step by step, linear process. It is a way of learning about the world through theapplication of knowledge. Scientists must be able to have an idea of what the answer to an investigation is. Scientistswill often make an observation and then form a hypothesis to explain why a phenomenon occurred. They use all oftheir knowledge and a bit of imagination in their journey of discovery.

Scientific investigations involve the collection of data through observation, the formation and testing of hypothesesby experimentation, and analysis of the results that involves reasoning.

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Scientific investigations begin with observations that lead to questions. We will use an everyday example to showwhat makes up a scientific investigation. Imagine that you walk into a room, and the room is dark.

• You observe that the room appears dark, and you question why the room is dark.• In an attempt to find explanations to this phenomenon, you develop several different hypotheses. One hypoth-

esis might state that the room does not have a light source at all. Another hypothesis might be that the lightsare turned off. Still, another might be that the light bulb has burnt out. Worse yet, you could be going blind.

• To discover the answer, you experiment. You feel your way around the room and find a light switch and turnit on. No light. You repeat the experiment, flicking the switch back and forth; still nothing.

• This means your first two hypotheses, that the room is dark because (1) it does not have a light source; and (2)the lights are off, have been rejected.

• You think of more experiments to test your hypotheses, such as switching on a flashlight to prove that you arenot blind.

• In order to accept your last remaining hypothesis as the answer, you could predict that changing the lightbulb will fix the problem. If your predictions about this hypothesis succeed (changing the light bulb fixes theproblem), the original hypothesis is valid and is accepted.

• However, in some cases, your predictions will not succeed (changing the light bulb does not fix the problem),and you will have to start over again with a new hypothesis. Perhaps there is a short circuit somewhere in thehouse, or the power might be out.

The general process of a scientific investigation is summed up in Figure 2.4.

FIGURE 2.4The general process of scientific investi-gations. A diagram that illustrates howscientific investigation moves from obser-vation of phenomenon to a theory. Theprogress is not as straightforward as itlooks in this diagram. Many times, everyhypothesis is falsified which means theinvestigator will have to start over again.

TABLE 2.1: Common Terms Used in Scientific Investigations

Term DefinitionScientific Method The process of scientific investigation.

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TABLE 2.1: (continued)

Term DefinitionObservation The act of noting or detecting phenomenon by the

senses. For example, taking measurements is a formof observation.

Hypotheses A suggested explanation based on evidence that can betested by observation or experimentation.

Scientific Reasoning The process of looking for scientific reasons for obser-vations.

Experiment A test that is used to rule out a hypothesis or validatesomething already known.

Rejected Hypothesis An explanation that is ruled out by experimentation.Confirmed Hypothesis An explanation that is not ruled out by repeated exper-

imentation, and makes predictions that are shown to betrue.

Inference Developing new knowledge based upon old knowledge.Theory A widely accepted hypothesis that stands the test of

time. Theories are often tested, and usually not re-jected.

Qualitative observation Data in the form of a sensory observationQuantitative observation Data in the form of a measured observation with units;

mass, volume, temperature, etc.Control A duplicate experiment except for the variable used for

comparasion.Variable Something that is changed in the experiment based on

the hypothesis.

The Scientific Method Made Easy explains scientific method succinctly and well (IE 1a, 1b, 1c, 1d, 1f,1g, 1j, 1k):http://www.youtube.com/watch?v=zcavPAFiG14&feature=related (9:55).


Making Observations

Scientists first make observations that raise questions. An observation is the act of noting or detecting phenomenonthrough the senses. For example, noting that a room is dark is an observation made through sight. An observationcan be qualitative or quantitiative. A qualitative observation is usually a written description of an observation andcan include color, shape, and/or smell. A quantitative observation is a measured observation.

Developing Hypotheses

In order to explain the observed phenomenon, scientists develop a number of possible explanations, or hypotheses.A hypothesis is a suggested explanation for a phenomenon or a suggested explanation for a relationship between

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many phenomena. Hypotheses are always based on evidence that can be tested by observation or experimentation.Scientific investigations are required to test hypotheses. Scientists mostly base hypotheses on prior observations oron extensions of existing scientific explanations.

A hypothesis is not really an educated guess. To define a hypothesis as "an educated guess" is like calling a tricyclea "vehicle with three." The definition leaves out the concept’s most important and characteristic feature: the purposeof hypotheses. People generate hypotheses as early attempts to explain patterns observed in nature or to predict theoutcomes of experiments. For example, in science, one could correctly call the following statement a hypothesis: Ifthe environment influences personality, then identical twins can have different personalities.

Evaluating Hypotheses

Scientific methods require hypotheses that are falsifiable, that is, they must be framed in a way that allows otherscientists to prove them false. Proving a hypothesis to be false is usually done by observation. However, confirmingor failing to falsify a hypothesis does not necessarily mean the hypothesis is true.

For example, a person comes to a new country and observes only white sheep. This person might form thehypothesis: “All sheep in this country are white.” This statement can be called a hypothesis, because it is falsifiable- it can be tested and proved wrong; anyone could falsify the hypothesis by observing a single black sheep, shownin Figure below. If the experimental uncertainties remain small (could the person reliably distinguish the observedblack sheep from a goat or a small horse), and if the experimenter has correctly interpreted the hypothesis, finding ablack sheep falsifies the "only white sheep" hypothesis. However, you cannot call a failure to find non-white sheepas proof that no non-white sheep exist.

Experiments

A scientific experiment must have the following features:

• a control, so variables that could affect the outcome are reduced• the variable being tested reflects the phenomenon being studied• the variable can be measured accurately, to avoid experimental error• the experiment must be reproducible.

An experiment is a test that is used to eliminate one or more of the possible hypotheses until one hypothesis remains.The experiment is a cornerstone in the scientific approach to gaining deeper knowledge about the physical world.Scientists use the principles of their hypothesis to make predictions, and then test them to see if their predictions areconfirmed or rejected.

Scientific experiments are usually run with the test and without the test to compare results. The experiment withoutthe test is the control.

A variable is a factor that can change over the course of an experiment. Independent variables are factors whosevalues are controlled by the experimenter to determine its relationship to an observed phenomenon (the dependentvariable). Dependent variables change in response to the independent variable. Controlled variables are alsoimportant to identify in experiments. They are the variables that are kept constant to prevent them from influencingthe effect of the independent variable on the dependent variable.

For example, if you were to measure the effect that different amounts of fertilizer have on plant growth, theindependent variable would be the amount of fertilizer used (the changing factor of the experiment). The dependentvariables would be the growth in height and/or mass of the plant (the factors that are influenced in the experiment).The controlled variables include the type of plant, the type of fertilizer, the amount of sunlight the plant gets, the sizeof the pots you use. The controlled variables are controlled by you, otherwise they would influence the dependentvariable.

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As a second example, say a scientist wants to determine if the type of light has a different effect on a moth beingattracted to light. The scientist controls the type of light (colored, incandescent, flourescent, neon, etc) - this wouldbe the independent variable of the experiment. How the moth responds to the different types of light would be thedependent variable.

In summary:

• The independent variable answers the question "What do I change?"• The dependent variables answer the question "What do I observe?"• The controlled variables answer the question "What do I keep the same?"

Experimental Design

Controlled Experiments

In an old joke, a person claims that they are snapping their fingers "to keep tigers away," and justifies their behaviorby saying, "See, it works!" While this experiment does not falsify the hypothesis "snapping your fingers keeps tigersaway," it does not support the hypothesis either, because not snapping your fingers will also keep tigers away. It alsofollows that not snapping your fingers will not cause tigers to suddenly appear (Figure 2.5).

FIGURE 2.5Are tigers really scared of snapping fingers, or is it more likely they are justnot found in your neighborhood? Considering which of the hypotheses ismore likely to be true can help you arrive at a valid answer. This principle,called Occam’s razor states that the explanation for a phenomenonshould make as few assumptions as possible. In this case, the hypothesis“there are no tigers in my neighborhood to begin with” is more likely,because it makes the least number of assumptions about the situation.

To demonstrate a cause and effect hypothesis, an experiment must often show that, for example, a phenomenonoccurs after a certain treatment is given to a subject, and that the phenomenon does not occur in the absence of thetreatment.

One way of finding this out is to perform a controlled experiment. In a controlled experiment, two identicalexperiments are carried out side-by-side. In one of the experiments the independent variable being tested is used, inthe other experiment, the control, or the independent variable is not used.

A controlled experiment generally compares the results obtained from an experimental sample against a controlsample. The control sample is almost identical to the experimental sample except for the one variable whose effectis being tested. A good example would be a drug trial. The sample or group receiving the drug would be theexperimental group, and the group receiving the placebo would be the control. A placebo is a form of medicine thatdoes not contain the drug that is being tested.

Controlled experiments can be conducted when it is difficult to exactly control all the conditions in an experiment. In

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this case, the experiment begins by creating two or more sample groups that are similar in as many ways as possible,which means that both groups should respond in the same way if given the same treatment.

Once the groups have been formed, the experimenter tries to treat them identically except for the one variable thathe or she wants to study (the independent variable). Usually neither the patients nor the doctor know which groupreceives the real drug, which serves to isolate the effects of the drug and allow the researchers to be sure the drugdoes work, and that the effects seen in the patients are not due to the patients believing they are getting better. Thistype of experiment is called a double blind experiment.

Controlled experiments can be carried out on many things other than people; some are even carried out in space! Thewheat plants in Figure 2.6 are being grown in the International Space Station to study the effects of microgravityon plant growth. Researchers hope that one day enough plants could be grown during spaceflight to feed hungryastronauts and cosmonauts. The investigation also measured the amount of oxygen the plants can produce in thehope that plants could become a cheap and effective way to provide oxygen during space travel.

FIGURE 2.6Spaceflight participant Anousheh Ansariholds a miniature wheat plant grown inthe Zvezda Service Module of the Inter-national Space Station.

Experiments Without Controls

The term experiment usually means a controlled experiment, but sometimes controlled experiments are difficultor impossible to do. In this case researchers carry out natural experiments. When scientists conduct a study innature instead of the more controlled environment of a lab setting, they cannot control variables such as sunlight,temperature, or moisture. Natural experiments therefore depend on the scientist’s observations of the system understudy rather than controlling just one or a few variables as happens in controlled experiments.

For a natural experiment, researchers attempt to collect data in such a way that the effects of all the variables canbe determined, and where the effects of the variation remains fairly constant so that the effects of other factors canbe determined. Natural experiments are a common research tool in areas of study where controlled experiments aredifficult to carry out. Examples include: astronomy -the study of stars, planets, comets, galaxies and phenomenathat originate outside Earth’s atmosphere, paleontology - the study of prehistoric life forms through the examinationof fossils, and meteorology - the study of Earth’s atmosphere.

In astronomy it is impossible, when testing the hypothesis "suns are collapsed clouds of hydrogen", to start out witha giant cloud of hydrogen, and then carry out the experiment of waiting a few billion years for it to form a sun.However, by observing various clouds of hydrogen in various states of collapse, and other phenomena related to thehypothesis, such as the nebula shown in Figure 2.7, researchers can collect data they need to support (or maybefalsify) the hypothesis.

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An early example of this type of experiment was the first verification in the 1600s that light does not travel fromplace to place instantaneously, but instead has a speed that can be measured. Observation of the appearance of themoons of Jupiter were slightly delayed when Jupiter was farther from Earth, as opposed to when Jupiter was closerto Earth. This phenomenon was used to demonstrate that the difference in the time of appearance of the moons wasconsistent with a measurable speed of light.

FIGURE 2.7The Helix nebula, located about 700 light-years away in the constellation Aquarius,belongs to a class of objects called plan-etary nebulae. Planetary nebulae are theremains of stars that once looked a lot likeour sun. When sun-like stars die, theypuff out their outer gaseous layers. Theselayers are heated by the hot core of thedead star, called a white dwarf, and shinewith infrared and visible colors. Scientistscan study the birth and death of starsby analyzing the types of light that areemitted from nebulae.

Natural Experiments

There are situations where it would be wrong or harmful to carry out an experiment. In these cases, scientists carryout a natural experiment, or an investigation without an experiment. For example, alcohol can cause developmentaldefects in fetuses, leading to mental and physical problems, through a condition called fetal alcohol syndrome.

Certain researchers want to study the effects of alcohol on fetal development, but it would be considered wrong orunethical to ask a group of pregnant women to drink alcohol to study its effects on their children. Instead, researcherscarry out a natural experiment in which they study data that is gathered from mothers of children with fetal alcoholsyndrome, or pregnant women who continue to drink alcohol during pregnancy. The researchers will try to reducethe number of variables in the study (such as the amount or type of alcohol consumed), which might affect their data.It is important to note that the researchers do not influence or encourage the consumption of alcohol; they collectthis information from volunteers.

Field Experiments

Field experiments are so named to distinguish them from lab experiments. Field experiments have the advantagethat observations are made in a natural setting rather than in a human-made laboratory environment. However, likenatural experiments, field experiments can get contaminated, and conditions like the weather are not easy to control.Experimental conditions can be controlled with more precision and certainty in the lab.

An introduction to the Prince William Sound Field Experiment can be seen at http://www.youtube.com/watch?v=O

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pQngP9HmKo (4:49).


Predictions

A prediction is a statement that tells what will happen under specific conditions. It can be expressed in the form: IfA is true, then B will also be true. Predictions are based on confirmed hypotheses shown to be true or not proved tobe false.

For researchers to be confident that their predictions will be useful and descriptive, their data must have as few errorsas possible. Accuracy is the measure of how close a calculated or measured quantity is to its actual value. Accuracyis closely related to precision, also called reproducibility or repeatability. Reproducibility and repeatability ofexperiments are cornerstones of scientific methods. If no other researcher can reproduce or repeat the results of acertain study, then the results of the study will not be accepted as valid. Results are called valid only if they are bothaccurate and precise.

A useful tool to help explain the difference between accuracy and precision is a target, shown in Figure 2.8. In thisanalogy, repeated measurements are the arrows that are fired at a target. Accuracy describes the closeness of arrowsto the bulls eye at the center. Arrows that hit closer to the bulls eye are more accurate. Arrows that are groupedtogether more tightly are more precise.

FIGURE 2.8A visual analogy of accuracy and preci-sion. Left target: High accuracy but lowprecision; Right target: low accuracy buthigh precision. The results of calculationsor a measurement can be accurate butnot precise; precise but not accurate; nei-ther accurate nor precise; or accurate andprecise. A collection of bulls eyes rightaround the center of the target would beboth accurate and precise.

Experimental Error

An error is a boundary on the precision and accuracy of the result of a measurement. Some errors are caused byunpredictable changes in the measuring devices (such as balances, rulers, or calipers), but other errors can be causedby reading a measuring device incorrectly or by using broken or malfunctioning equipment. Such errors can havean impact on the reliability of the experiment’s results; they affect the accuracy of measurements. For example, youuse a balance to obtain the mass of a 100 gram block. Three measurements that you get are: 93.1 g, 92.0 g, and 91.8g. The measurements are precise, as they are close together, but they are not accurate.

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If the cause of the error can be identified, then it can usually be eliminated or minimized. Reducing the numberof possible errors by careful measurement and using a large enough sample size to reduce the effect of errors willimprove the reliability of your results.

Scientific Theories

Scientific theories are hypotheses which have stood up to repeated attempts at falsification and are thus supportedby a great deal of data and evidence. Some well known biological theories include the theory of evolution by naturalselection, the cell theory (the idea that all organisms are made of cells), and the germ theory of disease (the idea thatcertain microbes cause certain diseases). The scientific community holds that a greater amount of evidence supportsthese ideas than contradicts them, and so they are referred to as theories.

In every day use, people often use the word theory to describe a guess or an opinion. For example, “I have a theoryas to why the light bulb is not working.” When used in this common way, “theory” does not have to be based onfacts, it does not have to be based on a true description of reality. This usage of the word theory often leads to amisconception that can be best summed up by the phrase "It’s not a fact, it’s only a theory." In such everyday usage,the word is most similar to the term hypothesis.

Scientific theories are the equivalent of what in everyday speech we would refer to as facts. In principle, scientifictheories are always subject to corrections or inclusion in another, wider theory. As a general rule for use of theterm, theories tend to deal with broader sets of phenomena than do hypotheses, which usually deal with much morespecific sets of phenomena or specific applications of a theory.

A video discussing the difference between a hypothesis and a theory (IE 1f) can be viewed at http://www.youtube.com/watch?v=jdWMcMW54fA (6:39).


Constructing Theories

In time, a confirmed hypothesis may become part of a theory or may grow to become a theory itself. Scientifichypotheses may be mathematical models. Sometimes they can be statements, stating that some particular instanceof the phenomenon under examination has some characteristic and causal explanations. These theories have thegeneral form of universal statements, stating that every instance of the phenomenon has a particular characteristic.

A hypothesis may predict the outcome of an experiment in a laboratory or the observation of a natural phenomenon.A hypothesis should also be falsifiable, and one cannot regard a hypothesis or a theory as scientific if it does notlend itself to being falsified, even in the future. To meet the “falsifiable” requirement, it must at least in principle bepossible to make an observation that would disprove the hypothesis. A falsifiable hypothesis can greatly simplify theprocess of testing to determine whether the hypothesis can be proven to be false. Scientific methods rely heavily onthe falsifiability of hypotheses by experimentation and observation in order to answer questions. Philosopher KarlPopper suggested that all scientific theories should be falsifiable; otherwise they could not be tested by experiment.

A scientific theory must meet the following requirements:

• it must be consistent with pre-existing theory in that the pre-existing theory has been experimentally verified,though it may often show a pre-existing theory to be wrong in an exact sense

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• it must be supported by many strands of evidence rather than a single foundation, ensuring that it is probablya good approximation, if not totally correct.

Also, a theory is generally only taken seriously if it:

• allows for changes to be made as new data are discovered, rather than claiming absolute certainty.• is the most straight forward explanation, and makes the fewest assumptions about a phenomenon (commonly

called “passing the Occam’s razor test”).

This is true of such established theories as special relativity, general relativity, quantum mechanics, plate tectonics,and evolution. Theories considered scientific meet at least most, but ideally all, of these extra criteria.

In summary, to meet the status of a scientific theory, the theory must be falsifiable or testable. Examples of scientifictheories in different areas of science include:

• Astronomy: Big Bang Theory• Biology: Cell Theory; Theory of Evolution; Germ Theory of Disease• Chemistry: Atomic Theory; Kinetic Theory of Gases• Physics: General Relativity; Special Relativity; Theory of Relativity; Quantum Field Theory• Earth Science: Giant Impact Theory; Plate Tectonics

Scientific Laws

Scientific laws are similar to scientific theories in that they are principles which can be used to predict the behaviorof the natural world. Both scientific laws and scientific theories are typically well-supported by observations and/orexperimental evidence. Usually scientific laws refer to rules for how nature will behave under certain conditions.Scientific theories are more overarching explanations of how nature works and why it exhibits certain characteristics.

A physical law or law of nature is a scientific generalization based on a sufficiently large number of empiricalobservations that it is taken as fully verified.

Isaac Newton’s law of gravitation is a famous example of an established law that was later found not to be univer-sal—it does not hold in experiments involving motion at speeds close to the speed of light or in close proximityof strong gravitational fields. Outside these conditions, Newton’s laws remain an excellent model of motion andgravity.

Scientists never claim absolute knowledge of nature or the behavior of the subject of the field of study. A scientifictheory is always open to falsification, if new evidence is presented. Even the most basic and fundamental theoriesmay turn out to be imperfect if new observations are inconsistent with them. Critical to this process is makingevery relevant part of research publicly available. This allows peer review of published results, and it also allowsongoing reviews, repetition of experiments and observations by many different researchers. Only by meeting theseexpectations can it be determined how reliable the experimental results are for possible use by others.

Lesson Summary

• Scientific skepticism questions claims based on their scientific verifiability rather than accepting claims basedon faith or anecdotes. Scientific skepticism uses critical thinking to analyze such claims and opposes claimswhich lack scientific evidence.

• Science is based on the analysis of things that humans can observe either by themselves through their senses,or by using special equipment. Science therefore cannot explain anything about the natural world that isbeyond what is observable by current means. Supernatural things cannot be explained by scientific means.

• Scientific investigations involve the collection of data through observation, the formation and testing ofhypotheses by experimentation, and analysis of the results that involves reasoning.

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• In a controlled experiment, two identical experiments are carried out side-by-side. In one of the experimentsthe independent variable being tested is used, in the other, the control, or the independent variable is not used.

• Any useful hypothesis will allow predictions based on reasoning. Reasoning can be broken down into twocategories: deduction and induction. Most reasoning in science is formed through induction.

• A variable is a factor that can change over the course of an experiment. Independent variables are factorswhose values are controlled by the experimenter to determine its relationship to an observed phenomenon (thedependent variable). Dependent variables change in response to the independent variable.

• Scientific theories are hypotheses which have stood up to repeated attempts at falsification and are thussupported by much data and evidence.

Review Questions

1. What is the goal of science?2. Distinguish between a hypothesis and a theory.3. The makers of two types of plant fertilizers claim that their product grows plants the fastest and largest. Design

an experiment that you could carry out to investigate the claims.4. Identify how hypotheses and predictions are related.5. What is the difference between the everyday term “theory” and the term “scientific theory?”6. Identify two ways that scientists can test hypotheses.7. Outline the difference between inductive and deductive reasoning.8. What is the range of processes that scientists use to carry out a scientific investigation called?9. To ensure that their results are not due to chance, scientists will usually carry out an experiment a number

of times, a process called replication. A scientist has two types of plants and she wants to test whichplant produces the most oxygen under sunny conditions outdoors. Devise a practical experimental approach,incorporating replication of the experiment.

10. In taking measurements, what is the difference between accuracy and precision?11. Name two features that a hypothesis must have, to be called a scientific hypothesis.12. Identify two features that a theory must have, to qualify as a scientific theory.13. Give an example of a superseded theory.14. Can a hypothesis take the form of a question? Explain your answer.15. Why is it a good idea to try to reduce the chances of errors happening in an experiment?

Further Reading / Supplemental Links

• http://www.nap.edu/readingroom/books/obas/• http://www.project2061.org/publications/sfaa/online/chap1.htm#inquiry• http://www.nasa.gov/mission_pages/station/science/experiments/PESTO.html#applications• http://biology.plosjournals.org/perlserv/?request=index-html&issn=1545-7885&ct=1• http://www.estrellamountain.edu/faculty/farabee/biobk/diversity.htm• http://www.nasa.gov/mission_pages/station/main/index.html• http://books.nap.edu/html/climatechange/summary.html• http://www.aaas.org/news/releases/2006/pdf/0219boardstatement.pdf

Vocabulary

accuracyThe measure of how close a calculated or measured quantity is to its actual value.

certain valueOr ’known’ value. The smallest marked line on any piece of measuring equipment.

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controlSomething that is not tested during the investigation.

controlled experimentTwo identical experiments are carried out side-by-side; in one of the experiments the independent variablebeing tested is used, in the other experiment, the control, or the independent variable is not used.

controlled variablesVariables that are kept constant to prevent influencing the effect of the independent variable on the dependentvariable.

deductionInvolves determining a single fact from a general statement.

dependent variableChanges in response to the independent variable.

experimentA test that is used to eliminate one or more of the possible hypotheses until one hypothesis remains.

hypothesisA suggested explanation based on evidence that can be tested by observation or experimentation.

independent variableFactor(s) whose values are controlled by the experimenter to determine its relationship to an observed phe-nomenon (the dependent variable).

inductionInvolves determining a general statement that is very likely to be true, from several facts.

meniscusThe curve in the upper surface of a liquid close to the surface of the container or other object.

observationThe act of noting or detecting phenomenon through the senses. For example, noting that a room is dark is anobservation made through sight.

Occam’s razorStates that the explanation for a phenomenon should make as few assumptions as possible.

phenomenonIs any occurrence that is observable.

precisionIs also called reproducibility; how close can the results of the experiment be repeated.

quantitative observationData in the form of a measured observation with units; mass, volume, temperature, etc.

qualitative observationData in the form of a sensory observation; sight, sound, smell, etc.

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reading scalesThe ability to directly read a measured number to its certain (known) value and interpret its uncertain (guess)value according to the scale of the device.

scientific methodsBased on gathering observable, empirical (produced by experiment or observation) and measurable evidencethat is critically evaluated.

scientific skepticismQuestions claims based on their scientific verifiability rather than accepting claims based on faith or anecdotes.

sensitivityThe minimum capactiy of a mechanical or simple measuring device to respond to stimulation.

uncertain valueAlso known as a ’guess’ value, and used when reading scales. The estimating of the unmarked measured valuebetween the two smallest or certain lints of a piece of measuring equipment. This is the last writen number,and is an order of magnitude smaller than the certain value.

variableA factor that can change over the course of an experiment.

Points to Consider

The Points to Consider section throughout this book is intended to have students think about material not yetpresented. These points are intended to lead students into the next lesson or chapter.

• Science is a particular way in which people examine and ask questions about the world. Can you think ofother ways in which people examine and ask questions about the world?

• Consider the importance of replication in an experiment and how replication of an experiment can affectresults.

• Scientists often disagree among themselves about scientific findings, and communicate such disagreement atscience conferences, through science articles in magazines, or science papers and in scientific journals. Canyou think of other ways in which scientists could communicate so that the public can get a better idea of whatthe “hot topics” in science are?

References

1. Star5112. http://www.flickr.com/photos/johnjoh/463607020/. CC-BY-SA2. NASA,PJLewis. http://commons.wikimedia.org/wiki/Image:Solar_sys.jpg,http://www.flickr.com/photos/pjlew

is/53056038/. Public Domain,CC-BY-SA3. Sebastian Ritter. http://en.wikipedia.org/wiki/Image:Streichholz.jpg. CC–BY-SA-2.54. Cnelson, Modified by: CK-12 Foundation. http://en.wikibooks.org/wiki/Image:Ap_biology_scienceofbiolo

gy01.jpg. Public Domain5. Malene Thyssen. http://en.wikibooks.org/wiki/Image:Siberian_Tiger_by_Malene_Th.jpg. GFDL6. NASA. http://commons.wikimedia.org/wiki/Image:Anousheh_Ansari_in_the_ISS.jpg. Public Domain7. NASA/JPL-Caltech/Univ. of Ariz. http://commons.wikimedia.org/wiki/Image:169141main_piaa09178.jpg.

Public Domain8. . http://en.wikipedia.org/wiki/Image:High_accuracy_Low_precision.svg, http://en.wikipedia.org/wiki/File:Hi

gh_precision_Low_accuracy.svg. Public Domain

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CHAPTER 3 Scope of Chemistry• Define chemistry.• Give examples of chemistry in everyday life.

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www.ck12.org Chapter 3. Scope of Chemistry

The Statue of Liberty, pictured above, is an icon of America and freedom. The statue is made of steel and coveredwith a thin layer of copper, the same type of matter that pennies are made of. Copper is a brownish red metal, sowhy is the statue green? Chemistry, which is a branch of physical science, has the answer.

What Is Chemistry?

Chemistry is the study of matter and energy and how they interact, mainly at the level of atoms and molecules.Basic concepts in chemistry include chemicals, which are specific types of matter, and chemical reactions. In achemical reaction, atoms or molecules of certain types of matter combine chemically to form other types of matter.All chemical reactions involve energy.

Q: How do you think chemistry explains why the copper on the Statue of Liberty is green instead of brownish red?

A: The copper has become tarnished. The tarnish—also called patina—is a compound called copper carbonate,which is green. Copper carbonate forms when copper undergoes a chemical reaction with carbon dioxide in moistair. The green patina that forms on copper actually preserves the underlying metal. That’s why it’s not removed fromthe statue. Some people also think that the patina looks attractive.

Chemistry and You

Chemistry can help you understand the world around you. Everything you touch, taste, or smell is made ofchemicals, and chemical reactions underlie many common changes. For example, chemistry explains how foodcooks, why laundry detergent cleans your clothes, and why antacid tablets relieve an upset stomach. Other examplesare illustrated in the Figure 3.1. Chemistry even explains you! Your body is made of chemicals, and chemicalchanges constantly take place within it.

Summary

• Chemistry is the study of matter and energy and how they interact, mainly at the level of atoms and molecules.Basic concepts in chemistry include chemicals and chemical reactions.

• Chemistry can help you understand the world around you. Everything you touch, taste, or smell is a chemical,and chemical reactions underlie many common changes.

Vocabulary

• chemistry: Study of the structure, properties, and interactions of matter, usually at the scale of atoms andmolecules.

Practice

Watch this video about the importance of chemistry, and then answer the questions below.

http://video.about.com/chemistry/What-Is-the-Importance-of-Chemistry-.htm

1. How is chemistry involved in medicines?2. Why is chemistry at the heart of environmental issues?3. Why is knowledge of chemistry important if you want to study other sciences?

Review

1. What is chemistry?

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FIGURE 3.1Each of these pictures represents a waythat chemicals and chemical reactions af-fect our lives.

2. Describe three ways that chemistry is important in your life.

References

1. Image copyright 0399778584, 2012; Image copyright dragon_fang, 2012; Image copyright restyler, 2012. .Used under license from Shutterstock.com

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www.ck12.org Chapter 4. Branches of Earth Science

CHAPTER 4 Branches of Earth Science

• Identify and define the major branches of Earth Science.

If science is the study of the natural world, what could be more obvious than to study the land, sky, water, andspace surrounding us?

Earth scientists seek to understand the beautiful sphere on which we live. Earth is a very large, complex system orset of systems, so most Earth scientists specialize in studying one aspect of the planet. Since all of the branches ofEarth science are connected, these researchers work together to answer complicated questions. The major branchesof Earth science are described below.

Geology

Geology is the study of the Earth’s solid material and structures and the processes that create them. Some ideasgeologists might consider include how rocks and landforms are created or the composition of rocks, minerals,or various landforms. Geologists consider how natural processes create and destroy materials on Earth, and howhumans can use Earth materials as resources, among other topics.

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FIGURE 4.1Geologists study rocks in the field to learnwhat they can from them.

Oceanography

Oceanography is the study of everything in the ocean environment, which covers about 70% of the Earth’s surface.Recent technology has allowed people and probes to venture to the deepest parts of the ocean, but much of the oceanremains unexplored. Marine geologists learn about the rocks and geologic processes of the ocean basins.

Climatology and Meteorology

Meteorology includes the study of weather patterns, clouds, hurricanes, and tornadoes. Using modern technologysuch as radars and satellites, meteorologists are getting more accurate at forecasting the weather all the time.

Climatology is the study of the whole atmosphere, taking a long-range view. Climatologists can help us betterunderstand how and why climate changes (Figure 4.2).

FIGURE 4.2Carbon dioxide released into the atmo-sphere is causing the global climate tochange.

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www.ck12.org Chapter 4. Branches of Earth Science

Environmental Science

Environmental scientists study the effects people have on their environment, including the landscape, atmosphere,water, and living things. Climate change is part of climatology or environmental science.

Astronomy

Astronomy is the study of outer space and the physical bodies beyond the Earth. Astronomers use telescopes to seethings far beyond what the human eye can see. Astronomers help to design spacecraft that travel into space and sendback information about faraway places or satellites (Figure 4.3).

FIGURE 4.3The Hubble Space Telescope.

Summary

• The study of Earth science includes many different fields, including geology, meteorology, oceanography, andastronomy.

• Each type of Earth scientist investigates the processes and materials of the Earth and beyond as a system.• Geology, climatology, meteorology, environmental science, and oceanography are important branches of Earth

science.

Making Connections


Practice

Use this resource to answer the questions that follow.

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1. What tools do geoscientists use?

2. Do all Earth scientists study Earth’s past?

3. What is fundamental about the study of Earth science?

4. Why is it important for people to study Earth science?

5. Why is Earth science called a combined science?

6. What issues will Earth science need to address in the future?

Review

1. What type of Earth scientist would be interested in understanding volcanic eruptions on the seafloor?

2. If it were to snow in Phoenix in July, which type of Earth scientist would be most surprised?

3. If people have been studying the natural world for centuries or even millennia, why are scientists learning somuch about Earth science now?

References

1. Image copyright Tom Grundy, 2011. . Used under license from Shutterstock.com2. Walter Siegmund. . CC-BY 2.53. Courtesy of NASA. The Hubble Space Telescope. Public Domain

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www.ck12.org Chapter 5. International System of Units

CHAPTER 5 International System ofUnits

• Describe the International System of Units (SI).• Convert units between International and English systems.

In 1999, NASA’s Mars Climate Orbiter, pictured here, burned up as it passed through Mars’ atmosphere. Thesatellite was programmed to orbit Mars at high altitude and gather climate data. Instead, the Orbiter flew too lowand entered the red planet’s atmosphere. Why did the Orbiter fly off course? The answer is human error. The flightsystem software on the Orbiter was written using scientific units of measurement, but the ground crew was enteringdata using common English units.

SI Units

The example of the Mars Climate Orbiter shows the importance of using a standard system of measurement inscience and technology. The measurement system used by most scientists and engineers is the International Systemof Units, or SI. There are a total of seven basic SI units, including units for length (meter) and mass (kilogram). SIunits are easy to use because they are based on the number 10. Basic units are multiplied or divided by powers often to arrive at bigger or smaller units. Prefixes are added to the names of the units to indicate the powers of ten, asshown in the Table 5.1.

TABLE 5.1: Prefixes of SI Units

Prefix Multiply Basic Unit ⇥ Basic Unit of Length = Meter (m)kilo- (k) 1000 kilometer (km) = 1000 mdeci- (d) 0.1 decimeter (dm) = 0.1 m

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Prefix Multiply Basic Unit ⇥ Basic Unit of Length = Meter (m)centi- (c) 0.01 centimeter (cm) = 0.01 mmilli- (m) 0.001 millimeter (mm) = 0.001 mmicro- (µ) 0.000001 micrometer (µm) = 0.000001 mnano- (n) 0.000000001 nanometer (nm) = 0.000000001 m

Q: What is the name of the unit that is one-hundredth (0.01) of a meter?

A: The name of this unit is the centimeter.

Q: What fraction of a meter is a decimeter?

A: A decimeter is one-tenth (0.1) of a meter.

Unit Conversions

In the table below, two basic SI units are compared with their English system equivalents. You can use theinformation in the table to convert SI units to English units or vice versa. For example, from the table you know that1 meter equals 39.37 inches. How many inches are there in 3 meters?

3 m = 3(39.37 in) = 118.11 in

TABLE 5.2: Unit Conversions

Measure SI Unit English Unit EquivalentLength meter (m) 1 m = 39.37 inMass kilogram (kg) 1 kg = 2.20 lb

Q: Rod needs to buy a meter of wire for a science experiment, but the wire is sold only by the yard. If he buys ayard of wire, will he have enough? (Hint: There are 36 inches in a yard.)

A: Rod needs 39.37 inches (a meter) of wire, but a yard is only 36 inches, so if he buys a yard of wire he won’t haveenough.

Accuracy

The accuracy of a measurement is how close the measurement is to the true value. If you were to hit fourdifferent golf balls toward an over-sized hole, all of them might land in the hole. These shots would all beaccurate because they all landed in the hole. This is illustrated in the Figure below.

Precision

As you can see from the Figure above, the four golf balls did not land as close to one another as they couldhave. Each one landed in a different part of the hole. Therefore, these shots are not very precise. The precisionof measurements is how close they are to each other. If you make the same measurement twice, the answersare precise if they are the same or at least very close to one another. The golf balls in the Figure below landedquite close together in a cluster, so they would be considered precise. However, they are all far from the hole,so they are not accurate.

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FIGURE 5.1

Q:If you were to hit four golf balls toward a hole and your shots were both accurate and precise, where wouldthe balls land?

A:All four golf balls would land in the hole (accurate) and also very close to one another (precise).

Measuring Length with a Metric Ruler

You’ve probably been using a ruler to measure length since you were in elementary school. But you may havemade most of the measurements in English units of length, such as inches and feet. In science, length is mostoften measured in SI units, such as millimeters and centimeters. Many rulers have both types of units, one oneach edge. The ruler pictured below has only SI units. It is shown here bigger than it really is so it’s easierto see the small lines, which measure millimeters. The large lines and numbers stand for centimeters. Countthe number of small lines from the left end of the ruler (0.0). You should count 10 lines because there are10 millimeters in a centimeter. When reading scales, we first need the reading of the smallest marked line- the certain, or ’known’ value. We finish reading the number with the uncertain or ’guess’ value; the spacebetween the two certain lines. The uncertain value is always one order of magnitude less than the certainvalue. In this example the certain value is the tenths of a cm, and the uncertain value would be reported to thehundredths of a cm. The units of the measurement are given in cm, the labeled units of the ruler.

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FIGURE 5.2

Q: What is the certain value?

A: The certain value is .2 cm

Q: What is the uncertain value?

A: The uncertain value is .20 cm.

Q: What is the final reading on the scale?

A: The correct reading is 3.20 cm

Measuring Mass with a Balance

Mass is the amount of matter in an object. Scientists often measure mass with a balance. A type of balancecalled a quad beam balance is pictured in the Figurebelow. To use this type of balance, follow these steps:

1. Place the object to be measured on the pan at the left side of the balance.

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FIGURE 5.3

FIGURE 5.4

2. Slide the movable masses to the right until the right end of the arm is level with the balance mark. Start bymoving the larger masses and then fine tune the measurement by moving the smaller masses as needed.

3. Read the three scales to determine the values of the masses that were moved to the right. Their combined massis equal to the mass of the object.

The Figure below is an enlarged version of the scales of the quadruple beam balance in Figure above. It allowsyou to read the scales. The top scale, which measures the largest movable mass, reads 100 grams. This is followedby the second scale, which reads 90 grams. The third scale reads seven grams, The bottom and smallest scale isread in three parts; tenths, hundredths, and thousandths of a gram. The printed number is the first decimal (tenths),the smallest line between the printed numbers (hundredths, also the certain value) is the second decimal, and theuncertain value (thousandths) found between the lines is the third decimal. The smallest beam reads .84 to the certainvalue, and about .848 to the uncertain value. Therefore the mass of the object in the pan is 197.848g (100g + 90g +7g + .8g +. 04g + .008g).

Q:What is the maximum mass this quadruple beam balance can measure?

A:The maximum mass it can measure is 311.00g (200g + 100g + 10g + 1.00g).

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FIGURE 5.5

FIGURE 5.6

FIGURE 5.7

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Q:What is the smallest mass this triple beam balance can measure?

A:The smallest mass it can measure is one-hundredth (0.01) of a gram.

To measure very small masses, scientists use electronic balances, like the one in the Figure below. This typeof balance also makes it easier to make accurate measurements because mass is shown as a digital readout. Inthe picture below, the balance is being used to measure the mass of a yellow powder on a glass dish. The massof the dish alone would have to be measured first and then subtracted from the mass of the dish and powdertogether. The difference between the two masses is the mass of the powder alone.

FIGURE 5.8

Measuring Volume with a Graduated Cylinder

At home, you might measure the volume of a liquid with a measuring cup. In science, the volume of a liquidmight be measured with a graduated cylinder, like the one sketched in the Figure below. The cylinder in thepicture has a scale in milliliters (mL), with a maximum volume of 100 mL. Volume can also be read in cm3,as 1 cm3 = 1mL.

We have three different graduated cylinders with two different readabilities. The 100 and 50mL cylinders arethe same and have a readability (certain value) of 1mL and an uncertain value of .1mL. The 10mL graduatedcuylinder has a certain value of .1mL and an uncertain value of .00 or .05mL, depending if the meniscus is onor off the line.

As a side note, our alcohol thermometers have a readability of 1oC. the uncertain value is either .0 or .5oC,depending if the end of red alcohol is on or off the line, as are the 10mL graduated cylinders.

Follow these steps when using a graduated cylinder to measure the volume of a liquid:

1. Place the cylinder on a level surface before adding the liquid.2. After adding the liquid, move so your eyes are at the same level as the top of the liquid in the cylinder.3. Read the mark on the glass that is at the lowest point of the curved surface of the liquid. This is called the

meniscus.

Q:What is the volume of the liquid in the graduated cylinder pictured above?

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FIGURE 5.9

A:The volume of the liquid is 67.0 mL.

Q:What would the measurement be if you read the highest point of the curved surface of the liquid by mistake?

A:The measurement would be 68.0 mL.

Summary

• The measurement system used by most scientists and engineers is the International System of Units, or SI.There are seven basic SI units, including units for length and mass.

• If you know the English equivalents of SI units, you can convert SI units to English units or vice versa.• In science, length may be measured with a metric ruler using SI units such as millimeters and centimeters.• Scientists measure mass with a balance, such as a triple beam balance or electronic balance.• In science, the volume of a liquid might be measured with a graduated cylinder.• Accuracy means making measurements that are close to the true value.• Precision means making measurements that are close in value to each other but not necessarily close to the

true value.

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Vocabulary

• SI: International System of Units, which is used by most scientists.• accuracy: Closeness of a measurement to the true value.• precision: Exactness of a measurement.• certain value: also ’known’ value; the smallest marked line on the scale• uncertain value: also ’guess’ value; the estimated measurement between the two certain lines at one order of

magnitude less then the certain value.

Practice

Do the interactive unit conversion quiz at this URL. You can check your answers online.

http://www.quia.com/quiz/2611894.html

A micrometer is a measuring device that is used to make precise measurements of very small distances. At the URLbelow, read about the parts of a micrometer and how to use it. Then test your skills by reading a virtual micrometer.Be sure to check your answers at the bottom of the test page. If you need more practice, click on the “Try more”link below the answers.

Review the concepts of accuracy and precision at this URL. Then play the dart game until you obtain scores that areboth accurate and precise.

http://interactagram.com/physics/PrecisionAndAccuracy/

Review

1. What does SI stand for?2. Why is it important for scientists and engineers to adopt a common system of measurement units?3. How many grams equal 1 kilogram?4. What fraction of a meter is a millimeter?5. How many pounds equal 5 kilograms?6. Complete this statement: A measurement is accurate when it is __________.7. What makes two measurements precise?8. Kami measured the volume of a liquid three times and got these results: 66.71 mL, 66.70 mL, 66.69 mL. The

actual volume of the liquid is 69.70 mL. Are Kami’s measurements precise? Are they accurate? Explain youranswers.

9. Using the enlarged metric ruler segment shown below, what is the length of the blue line in centimeters?

1. Assume that an object has been placed in the pan of a triple beam balance. The scales of the balance are shownbelow. What is the mass of the object?

1. What is the weight measured on the balance?2. How much liquid does this graduated cylinder contain?

References

1. CK-12 Foundation. . CCSA

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FIGURE 5.10

FIGURE 5.11

2. CK-12 Foundation. . CCSA3. . . CC BY-NC-SA4. . . CC BY-NC-SA5. CK-12 Foundation. . CCSA6. . . CC BY-NC-SA7. CK-12 Foundation. . CCSA8. CK-12 Foundation. . CCSA9. CK-12 Foundation. . CCSA

10. . . CC BY-NC-SA11. . . CC BY-NC-SA12. CK-12 Foundation. . CCSA

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FIGURE 5.12

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CHAPTER 6 Matter, Mass, Weight, andVolume

• Define matter.• State what mass measures.• State what volume measures.

Can you guess what this colorful image shows? Believe it or not, it actually depicts individual atoms of iron (blue) ona surface of copper atoms (red). The image was created with an extremely powerful microscope, called a scanningtunneling microscope. This is the only type of microscope that can make images of things as small as atoms, thebasic building blocks of matter.

What’s the Matter?

Matter is all the “stuff” that exists in the universe. Everything you can see and touch is made of matter, includingyou! The only things that aren’t matter are forms of energy, such as light and sound. In science, matter is definedas anything that has mass and volume. Mass and volume measure different aspects of matter.

Mass and Weight

Mass is a measure of the amount of matter in a substance or an object. The basic SI unit for mass is the kilogram(kg), but smaller masses may be measured in grams (g). To measure mass, you would use a balance. In the lab,

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www.ck12.org Chapter 6. Matter, Mass, Weight, and Volume

mass may be measured with a quadruple beam balance or an electronic balance, but the old-fashioned balance in theFigure 6.1 may give you a better idea of what mass is. If both sides of this balance were at the same level, it wouldmean that the fruit in the left pan has the same mass as the iron object in the right pan. In that case, the fruit wouldhave a mass of 1 kg, the same as the iron. As you can see, however, the fruit is at a higher level than the iron. Thismeans that the fruit has less mass than the iron, that is, the fruit’s mass is less than 1 kg.

Q: If the fruit were at a lower level than the iron object, what would be the mass of the fruit?

A: The mass of the fruit would be greater than 1 kg.

FIGURE 6.1

Mass is commonly confused with weight. The two are closely related, but they measure different things. Whereasmass measures the amount of matter in an object, weight measures the force of gravity acting on an object. Theforce of gravity on an object depends on its mass but also on the strength of gravity. If the strength of gravity is heldconstant (as it is all over Earth), then an object with a greater mass also has a greater weight.

Q: With Earth’s gravity, an object with a mass of 1 kg has a weight of 2.2 lb. How much does a 10 kg object weighon Earth?

A: A 10 kg object weighs ten times as much as a 1 kg object:

10 ⇥ 2.2 lb = 22 lb

The mass of an object is measured in kilograms and will be the same whether it is measured on the earth or on themoon. The weight of an object on the earth is defined as the force acting on the object by the earth’s gravity. If theobject were sitting on the moon, then its weight on the moon would be the force acting on the object by the moon’sgravity. Weight is measured by a spring scale that has been calibrated for wherever the scale is placed and it readsin Newtons.

The force of gravity is given by Newton’s Second Law, F = ma, when F is the force of gravity in Newtons, m isthe mass of the object in kilograms, and a is the acceleration due to gravity, 9.80 m/s2. When the formula is usedspecifically for finding weight from mass or vice versa, it may appear as W = mg.

Example:

Q: If a 100 kg person stook on Mars, how much would they weigh in Newtons if Mars’ gravity is 38% of Earth’sgravity.

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A. W = mg,

W= 100 * (0.38)

W= 38 N

Volume

Volume is a measure of the amount of space that a substance or an object takes up. The basic SI unit for volume isthe cubic meter (m3), but smaller volumes may be measured in cm3, and liquids may be measured in liters (L) ormilliliters (mL). How the volume of matter is measured depends on its state.

• The volume of a liquid is measured with a measuring container, such as a measuring cup or graduated cylinder.• The volume of a gas depends on the volume of its container: gases expand to fill whatever space is available

to them.• The volume of a regularly shaped solid can be calculated from its dimensions. For example, the volume of a

rectangular solid is the product of its length, width, and height.• The volume of an irregularly shaped solid can be measured by the displacement method. You can read below

how this method works. For a video on the displacement method, go to this URL: http://www.youtube.com/watch?v=q9L52maq_vA.

Q: How could you find the volume of air in an otherwise empty room?

A: If the room has a regular shape, you could calculate its volume from its dimensions. For example, the volume ofa rectangular room can be calculated with the formula:

Volume = length ⇥ width ⇥ height

If the length of the room is 5.0 meters, the width is 3.0 meters, and the height is 2.5 meters, then the volume of theroom is:

Volume = 5.0 m ⇥ 3.0 m ⇥ 2.5 m = 37.5 m3

FIGURE 6.2

Q: What is the volume of the dinosaur in the Figure 6.2?

A: The volume of the water alone is 4.8 mL. The volume of the water and dinosaur together is 5.6 mL. Therefore,the volume of the dinosaur alone is 5.6 mL – 4.8 mL = 0.8 mL.

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www.ck12.org Chapter 6. Matter, Mass, Weight, and Volume

Summary

• Matter is all the “stuff” that exists in the universe. It has both mass and volume.• Mass measures the amount of matter in a substance or an object. The basic SI unit for mass is the kilogram

(kg).• Volume measures the amount of space that a substance or an object takes up. The basic SI unit for volume is

the cubic meter (m3).• The weight of an object on the earth is defined as the force acting on the object by the earth’s gravity• Weight is measured by a calibrated spring scale.• The formula relating mass and weight is W = mg.

Vocabulary

• mass: Amount of matter in a substance or object.• matter: Anything that has mass and volume.• volume: Amount of space taken up by matter.

Practice

Do the mass and volume quiz at this URL. Be sure to check your answers.

http://www.proprofs.com/quiz-school/story.php?title=measurement-mass-volume

A song about the difference between mass and weight sung by Mr. Edmunds to the tune of Sweet Caroline. Re-member to make allowances for the fact that he is a teacher, not a profession singer. Use this resource to answer thequestions that follow.


1. What is used to measure mass?2. What is used to measure weight?3. What units are used to measure mass?4. What units are used to measure weight?

This video shows what appears to be a magic trick but is actually a center of gravity demonstration.

http://www.darktube.org/watch/simple-trick-magic-no-physics

Review

1. How do scientists define matter?2. What is mass? What is the basic SI unit of mass?3. What does volume measure? Name two different units that might be used to measure volume.4. Explain how to use the displacement method to find the volume of an irregularly shaped object.

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References

1. Image copyright Dimitar Sotirov, 2012. . Used under license from Shutterstock.com2. CK-12 Foundation - Christopher Auyeung. . CC-BY-NC-SA 3.0

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www.ck12.org Chapter 7. Significant Figures

CHAPTER 7 Significant Figures• Define significant figures.• State rules for counting significant figures.• Explain how to determine significant figures in calculations.• Identify rules for rounding numbers.

Jerod has a homework problem that involves finding the area of a rectangle. He knows that the area of a rectangleequals its length times its width. The rectangle in question has a length of 6.9 m and a width of 6.8 m, so hemultiplies the two numbers on his calculator. The answer he gets is 46.92 m2, which he records on his homework.To his surprise, his teacher marks this answer wrong. The reason? The answer has too many significant figures.

What Are Significant Figures?

In any measurement, the number of significant figures, also called significant digits, is the number of digits thoughtto be correct by the person doing the measuring. It includes all digits that can be read directly from the measuringdevice plus one estimated digit.

Look at the sketch of a beaker in the Figure 7.1. How much blue liquid does the beaker contain? The top of theliquid falls between the mark for 40 mL and 50 mL, but it’s closer to 50 mL. A reasonable estimate is 47 mL. In thismeasurement, the first digit (4) is the certain value and the second digit (7) is an estimate or the uncertain value, sothe measurement has two significant figures.

Now look at the graduated cylinder sketched in the Figure 7.2. How much blue liquid does it contain? First, it’simportant to note that you should read the amount of liquid at the bottom of its curved surface, called the meniscus.

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FIGURE 7.1

This falls about half way between the mark for 36 mL and the mark for 37 mL, so a reasonable estimate would be36.5 mL.

Q: How many significant figures does this measurement have?

A: There are three significant figures in this measurement. You know that the first two digits (3 and 6) are accurate.The third digit (5) is an estimate. Remember the readability; the 6 is the certain value, and the 5 the uncertain.

Rules for Counting Significant Figures

The examples above show that it’s easy to count the number of significant figures when you are making a measure-ment. But what if someone else has made the measurement? How do you know which digits are known for certainand which are estimated? How can you tell how many significant figures there are in the measurement? There areseveral rules for counting significant figures:

TABLE 7.1:

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Rules for SIGNIFICANT DIGITS (Figures)

• When you multiply or divide numbers, a calculator will give you more digits than you could possiblymeasure; “significant digits” is the scientific method of limiting the number of digits in a calculated answer.

• Significant digits are only used when multiplying or dividing; with addition or subtraction, simply keep thesmallest number of decimals that was in your original math.

• The “rule of thumb” for significant digits is that your answer will have the same number of significant digitsas the number with the least number of digits.

• What makes a number significant?

– Any non-zero number– Any non-placeholder or spacer zero.

• When is zero not significant?

1. Spacer zeros, or placeholders, are not significant. These zeros hold a numbers “place” to the correctdecimal. If a number can be written in scientific notation without the zero, it is not significant.

2. The simplest way to remember is that every number is significant except a spacer/placeholder zero.

Examples:

1. 50.05 = 4 significant digits (sandwich rule).2. 470.50 = 5 significant digits (ending decimal 0 is always significant).3. 0.404 = 3 significant digits (first 0 is a placeholder).4. 0.004 = 1 significant digits (3 placeholder zeros).5. 0.040 = 2 significant digits (2 placeholder zeros).6. 0.400 = 3 significant digits (1 placeholder zeros).7. 400. = 3 significant digits (decimal)8. 400 = a counting number; infinite significant digits (ignore for SD total)9. 0.23 and 0.023 both have 2 significant digits

10. 408,300 - 4 signigicant digits (there is no decimal; the last two zeros are placeholders)

*Whenever you see 0.***, you are dealing with AT LEAST one spacer zero.*Round at the appropriate significant digit based on the next number (5+).Sample problems:

1. 2022.5 ÷ 3.5 = 2SD = 577.8571 = 580 no decimal; 0 is a placeholder. (580. = 3SD.)2. 0.790 ÷ 450.0 = 3SD = 0.0017555 = .00176; 2 placeholders needed for math but do not count towards

total3. 320.7 + 62.24 = 1 decimal = 382.94 = 382.94. 10.2 x 10.4 = 3SD = 106.08 = 106.

After your math, start at the first SD, count out the number of SD’s from the left, then stop and round at the lastSD. Remember your answer cannot have more digits than the number with the fewest digits in your math (ordecimals if +/-). (2012)

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FIGURE 7.2

Q: How many significant figures are there in each of these numbers: 20,080, 2.080, and 2000?

A: Both 20,080 and 2.080 contain four significant figures, but 2000 has just one significant figure as it is considereda ’counting number’.

Determining Significant Figures in Calculations

When measurements are used in a calculation, the answer cannot have more significant figures than the measurementwith the fewest significant figures. This explains why the homework answer above is wrong. It has more significantfigures than the measurement with the fewest significant figures. As another example, assume that you want to

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calculate the volume of the block of wood shown in the Figure 7.3.

FIGURE 7.3

The volume of the block is represented by the formula:

Volume = length ⇥ width ⇥ height

Therefore, you would do the following calculation:

Volume = 1.0 cm ⇥ 1.0 cm ⇥ 1.0 cm = 1 cm3

Q: Does this answer have the correct number of significant figures?

A: No, it has too few significant figures. The correct answer is 1.0 cm3. That’s because each measurement has twosignificant figures. Therefore, we must add a zero so the answer can have two significant figures.

Rules for Rounding

To get the correct answer in the volume calculation above, adding a significant digit was necessary. Sometimes itis necessary to round an answer. Rounding is done when one or more ending digits are dropped to get the correctnumber of significant figures. In this example, if the numbers were 1.2 cm, 1.0 cm, and 1 cm the answer would havebeen calculated to 1.2 cm3, but the final answer would rounded down to a lower number, from 1.2 to 1, as the 1 hadonly one and the fewest number of significant figures. Sometimes the answer is rounded up to a higher number. Howdo you know which way to round? Follow these simple rules:

• If the digit to be rounded (dropped) is less than 5, then round down. For example, when rounding 2.344 tothree significant figures, round down to 2.34.

• If the digit to be rounded is greater than 5, then round up. For example, when rounding 2.346 to threesignificant figures, round up to 2.35.

• If the digit to be rounded is 5, round up if the digit before 5 is odd, and round down if digit before 5 is even. Forexample, when rounding 2.345 to three significant figures, round down to 2.34. This rule may seem arbitrary,but in a series of many calculations, any rounding errors should cancel each other out.

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Summary

• In any measurement, the number of significant figures is the number of digits thought to be correct by theperson doing the measuring. It includes all digits that can be read directly from the measuring device plus oneestimated digit.

• To determine the number of significant figures in a measurement that someone else has made, follow the rulesfor counting significant figures.

• When measurements are used in a calculation, the answer cannot have more significant figures than themeasurement with the fewest significant figures.

• Rounding is done when one or more ending digits are dropped to get the correct number of significant figures.Simple rules state when to round up and when to round down.

Vocabulary

• significant figures (digits): Correct number of digits in an answer that is based on the least precise measure-ment used in the calculation.

Practice

Do the significant figures quiz at this URL. Be sure to check your answers.

http://www.sciencegeek.net/APchemistry/APtaters/sigfigs.htm

Review

1. How do you determine the number of significant figures when you make a measurement?2. Measure the width of a sheet of standard-sized (8.5 in x 11.0 in) loose-leaf notebook paper. Make the

measurement in centimeters and express the answer with the correct number of significant figures.3. How many significant figures do each of these measurements have?

a. 0.04b. 500c. 1.50

4. In this calculation, how many significant figures should there be in the answer? 1.0234 + 1.1 + 0.00565. Round each of these numbers to three significant figures:

a. 1258b. 3274c. 6845

References

1. CK-12 Foundation - Zachary Wilson. . CC-BY-NC-SA 3.02. CK-12 Foundation - Zachary Wilson. . CC-BY-NC-SA 3.03. CK-12 Foundation - Zachary Wilson. . CC-BY-NC-SA 3.0

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www.ck12.org Chapter 8. Calculating Derived Quantities

CHAPTER 8 Calculating DerivedQuantities

• Define derived quantity.• Explain how to calculate area, volume, and density.• Identify units of area, volume, and density.

COMBINE CHAPTER 9 WITH CHAPTER 10.

This scientist is using a calculator. Doing science often requires calculations. Converting units—say from inchesto centimeters—is one type of calculation that might be required. Calculations may also be needed to find derivedquantities.

What Are Derived Quantities?

Derived quantities are quantities that are calculated from two or more measurements. Derived quantities cannot bemeasured directly. They can only be computed. Many derived quantities are calculated in physical science. Threeexamples are area, volume, and density.

Calculating Area

The area of a surface is how much space it covers. It’s easy to calculate the area of a surface if it has a regular shape,such as the blue rectangle in the sketch below. You simply substitute measurements of the surface into the correctformula. To find the area of a rectangular surface, use this formula:

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Area (rectangular surface) = length ⇥ width (l ⇥ w)

Q: What is the area of the blue rectangle?

A: Substitute the values for the rectangle’s length and width into the formula for area:

Area = 9 cm ⇥ 5 cm = 45 cm2

While technically a violation of significant figures, you are allowed enough digits to make an answer mathemati-

cally correct; 45 is correct to the whole number. The volume calculations below are similar.

Q: Can you use this formula to find the area of a square surface?

A: Yes, you can. A square has four sides that are all the same length, so you would substitute the same value forboth length and width in the formula for the area of a rectangle.

Calculating Volume

The volume of a solid object is how much space it takes up. It’s easy to calculate the volume of a solid if it has asimple, regular shape, such as the rectangular solid pictured in the sketch below. To find the volume of a rectangularsolid, use this formula:

Volume (rectangular solid) = length ⇥ width ⇥ height (l ⇥ w ⇥ h)

Q: What is the volume of the blue rectangular solid?

A: Substitute the values for the rectangular solid’s length, width, and height into the formula for volume:

Volume = 10 cm ⇥ 3 cm ⇥ 5 cm = 150 cm3

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www.ck12.org Chapter 8. Calculating Derived Quantities

Calculating Density

Density is a quantity that expresses how much matter is packed into a given space. The amount of matter is its mass,and the space it takes up is its volume. To calculate the density of an object, then, you would use this formula:

Density =mass

volume

Q: The volume of the blue rectangular solid above is 150 cm3. If it has a mass of 300 g, what is its density?

A: The density of the rectangular solid is:

Density =300 g

150 cm3 = 2 g/cm3

Technically, the answer should be 2.0 g/cm3. 300 has one significant figure as a counting number and is notused in the calculations. 150 has two significant figures, so we need to add a 0 to get the second digit.

Q: Suppose you have two boxes that are the same size but one box is full of feathers and the other box is full ofbooks. Which box has greater density?

A: Both boxes have the same volume because they are the same size. However, the books have greater mass thanthe feathers. Therefore, the box of books has greater density.

Units of Derived Quantities

A given derived quantity, such as area, is always expressed in the same type of units. For example, area is alwaysexpressed in squared units, such as cm2 or m2. If you calculate area and your answer isn’t in squared units, then youhave made an error.

Q: What units are used to express volume?

A: Volume is expressed in cubed units, such as cm3 or m3.

Q: A certain derived quantity is expressed in the units kg/m3. Which derived quantity is it?

A: The derived quantity is density, which is mass (kg) divided by volume (m3).

Summary

• Derived quantities are quantities that are calculated from two or more measurements. They include area,volume, and density.

• The area of a rectangular surface is calculated as its length multiplied by its width.• The volume of a rectangular solid is calculated as the product of its length, width, and height.• The density of an object is calculated as its mass divided by its volume.• A given derived quantity is always expressed in the same type of units. For example, area is always expressed

in squared units, such as cm2.

Practice

Read about derived quantities at this URL, and then answer the questions below.

http://faculty.wwu.edu/vawter/PhysicsNet/Topics/ModelsInScience/Units/UnitsInScience.html

1. Identify six fundamental units in physical science.

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2. What is speed? How is it calculated? What are its SI units? (Hint: The symbol D represents a difference, orchange, in a unit. For example, Dt represents a change in time.)

3. Which derived quantity equals force divided by area?

Review

1. What is a derived quantity? Give an example.2. What are the dimensions of a square that has an area of 4 cm2?3. Explain how you would calculate the volume of a cube.4. Which derived quantity is used to calculate density?5. Which derived quantity might be measured in mm3?

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www.ck12.org Chapter 9. Scientific Graphing

CHAPTER 9 Scientific Graphing• State why graphs are useful in science.• Describe bar graphs and their uses.• Describe circle graphs and what they show.• Describe line graphs and how they are used.

Tornadoes, like the one pictured here, are very powerful storms that can cause incredible destruction. Their windsmay exceed 300 miles per hour, and they can completely level towns and neighborhoods in just minutes. Becausetornadoes can be so serious, they are closely monitored, measured, and counted. As a result, there are a lot of dataon tornadoes. One way to present these data is with graphs.

Using Graphs in Science

Graphs are very useful tools in science. They can help you visualize a set of data. With a graph, you can actuallysee what all the numbers in a data table mean. Three commonly used types of graphs are bar graphs, circle graphs,and line graphs. Each type of graph is suitable for showing a different type of data.

Bar Graphs

The data in Table 9.1 shows the average number of tornadoes per year for the ten U.S. cities that have the mosttornadoes. The data were averaged over the time period 1950–2007.

TABLE 9.1: Average Number of Tornadoes per Year (1950–2007) in U.S. Cities with the GreatestNumber of Tornadoes

Rank City Average Number of Tornadoes(per1000 Square Miles)

1 Clearwater, FL 7.4

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Rank City Average Number of Tornadoes(per1000 Square Miles)

2 Oklahoma City, OK 2.23 Tampa-St. Petersburg, FL 2.14 Houston, TX 2.15 Tulsa, OK 2.16 New Orleans, LA 2.07 Melbourne, FL 1.98 Indianapolis, IN 1.79 Fort Worth, TX 1.710 Lubbock, TX 1.6

Bar graphs are especially useful for comparing values for different things, such as the average numbers of tornadoesfor different cities. Therefore, a bar graph is a good choice for displaying the data in theTable 9.1. The bar graph inFigure 9.1 shows one way that these data could be presented.

FIGURE 9.1

Q: What do the two axes of this bar graph represent?

A: The x-axis represents cities, and the y-axis represents average numbers of tornadoes.

Q: Could you switch what the axes represent? If so, how would the bar graph look?

A: Yes; the x-axis could represent average numbers of tornadoes, and the y-axis could represent cities. The bars ofthe graph would be horizontal instead of vertical.

Circle Graphs

The data in Table 9.2 shows the percent of all U.S. tornadoes by tornado strength for the years 1986 to 1995. In thistable, tornadoes are rated on a scale called the F scale. On this scale, F0 tornadoes are the weakest and F5 tornadoesare the strongest.

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TABLE 9.2: Percent of Tornadoes by Strength in the U.S. (1986–1995)

Tornado Scale(F-scalerating)

Percent of all U.S. Torna-does

F0 55.0%F1 31.6%F2 + F3 2.6%F4 0.7%F5 0.1%

Circle graphs are used to show percents (or fractions) of a whole, such as the percents of F0 to F5 tornadoes out ofall tornadoes. Therefore, a circle graph is a good choice for the data in the table. The circle graph in the Figure 9.2displays these data.

FIGURE 9.2

Q: What if the above data table on tornado strength listed the numbers of tornadoes rather than the percents oftornadoes? Could a circle graph be used to display these data?

A: No, a circle graph can only be used to show percents (or fractions) of a whole. However, the numbers could beused to calculate percents, which could then be displayed in a circle graph. If you need a refresher on percents andfractions, go to this URL: http://www.mathsisfun.com/decimal-fraction-percentage.html.

Line Graphs

Consider the data in Table 9.3. It lists the number of tornadoes in the U.S. per month, averaged over the years 2009to 2011.

TABLE 9.3: Average Number of Tornadoes in the U.S. per Month (2009–2011)

Month Average Number of TornadoesJanuary 17February 33March 74April 371May 279June 251

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Month Average Number of TornadoesJuly 122August 57September 39October 65November 39December 34

Line graphs are especially useful for showing changes over time, or time trends in data, such as how the averagenumber of tornadoes varies throughout the year. Therefore, a line graph would be a good choice to display the datain the Table 9.3. The line graph in the Figure 9.3 shows one way this could be done.

FIGURE 9.3

Q: Based on the line graph above, describe the trend in tornado numbers by month throughout the course of a year.

A: The number of tornadoes rises rapidly from a low in January to a peak in April. This is followed by a relativelyslow decline throughout the rest of the year.

Summary

• Graphs are very useful tools in science because they display data visually. Three commonly used types ofgraphs are bar graphs, circle graphs, and line graphs. Each type of graph is suitable for a different type of data.

• Bar graphs are suitable for comparing values for different things, such as the average numbers of tornadoesfor different cities.

• Circle graphs are used to show percents of a whole, such as the percent of all U.S. tornadoes with differentstrengths.

• Line graphs are especially useful for showing changes over time, such as variation in the number of tornadoesby month throughout the year.

Practice

When you make a line graph, you need to locate x and y values on a set of axes. This lets you plot the points thatwill be connected to create the line. Do the frog-and-fly activity at the following URL. See how many flies you cancatch while you practice plotting points.

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http://hotmath.com/hotmath_help/games/ctf/ctf_hotmath.swf

Review

1. What is the advantage of displaying data in a graph rather than just listing data in a table?2. Explain what a circle graph shows.3. Examine the data in Table 9.4. Which type of graph would you use to display the data? Why would you use

this type of graph?

TABLE 9.4: Average Number of Tornadoes per Year in Selected States (1961-1990)

State Average Number of TornadoesCalifornia 4Idaho 2Kentucky 10Michigan 18Montana 5North Carolina 14North Dakota 20Tennessee 12

4. Using a sheet of graph paper, create a graph of the data in question 3. Use the type of graph you identified inyour answer to question 3.

References

1. CK-12 Foundation. . CC-BY-NC-SA 3.02. CK-12 Foundation. . CC-BY-NC-SA 3.03. CK-12 Foundation. . CC-BY-NC-SA 3.0

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CHAPTER 10 Scientific NotationHere you’ll learn how to use scientific notation to rewrite very large or very small numbers as the product of adecimal and 10 raised to a specific power.

Did you know that the average distance of the Earth from the Sun is about 92,000,000 miles? This is a big number!Do you think that there is any way to write it more compactly? In this Concept, you’ll learn all about using scientificnotation so that you can express very large or very small numbers as the product of a decimal and 10 to a certainpower. This way, you’ll be able to express numbers such as 92,000,000 miles much more succinctly.

Guidance

Sometimes in mathematics numbers are huge. They are so huge that we use what is called scientific notation. It iseasier to work with such numbers when we shorten their decimal places and multiply them by 10 to a specific power.In this Concept, you will learn how to express numbers using scientific notation.

Definition: A number is expressed in scientific notation when it is in the form

N ⇥10n

where 1 N < 10 and n is an integer.

For example, 2.35⇥ 1037 is a number expressed in scientific notation. Notice there is only one number in front ofthe decimal place.

Since the scientific notation uses powers of ten, we want to be comfortable expressing different powers of ten.

Powers of 10:

100,000 = 105

10,000 = 104

1,000 = 103

100 = 102

10 = 101

Using Scientific Notation for Large Numbers

If we divide 643,297 by 100,000 we get 6.43297. If we multiply 6.43297 by 100,000, we get back to our originalnumber, 643,297. But we have just seen that 100,000 is the same as 105, so if we multiply 6.43297 by 105, weshould also get our original number, 643,297, as well. In other words 6.43297⇥105 = 643,297. Because there arefive zeros, the decimal moves over five places.

Example A

Look at the following examples:

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2.08⇥104 = 20,800

2.08⇥103 = 2,080

2.08⇥102 = 208

2.08⇥101 = 20.8

2.08⇥100 = 2.08

The power tells how many decimal places to move; positive powers mean the decimal moves to the right. A positive4 means the decimal moves four positions to the right.

Example B

Write in scientific notation.

653,937,000

Solution:

653,937,000 = 6.53937000⇥100,000,000 = 6.53937⇥108

Oftentimes, we do not keep more than a few decimal places when using scientific notation, and we round the numberto the nearest whole number, tenth, or hundredth depending on what the directions say. Rounding Example A couldlook like 6.5⇥108.

Using Scientific Notation for Small Numbers

We’ve seen that scientific notation is useful when dealing with large numbers. It is also good to use when dealingwith extremely small numbers.

Example C

Look at the following examples:

2.08⇥10�1 = 0.208

2.08⇥10�2 = 0.0208

2.08⇥10�3 = 0.00208

2.08⇥10�4 = 0.000208

Guided Practice

The time taken for a light beam to cross a football pitch is 0.0000004 seconds. Write in scientific notation.

Solution:

0.0000004 = 4⇥0.0000001 = 4⇥ 110,000,000 = 4⇥ 1

107 = 4⇥10�7

Practice

Sample explanations for some of the practice exercises below are available by viewing the following video. Notethat there is not always a match between the number of the practice exercise in the video and the number of the

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practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra:Scientific Notation (14:26)


Write the numerical value of the following expressions.

1. 3.102⇥102

2. 7.4⇥104

3. 1.75⇥10�3

4. 2.9⇥10�5

5. 9.99⇥10�9

Write the following numbers in scientific notation.

6. 120,0007. 1,765,2448. 639. 9,654

10. 653,937,00011. 1,000,000,00612. 1213. 0.0028114. 0.00000002715. 0.00316. 0.00005617. 0.0000500718. 0.00000000000954

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