video 2-1 scientific method units of measurement metric conversions
TRANSCRIPT
Video 2-1
Scientific Method Units of Measurement Metric Conversions
Chapter 2
MEASUREMENT AND CALCULATIONS
I. Scientific Method
logical approach to problem solving
I. Scientific Method
Basic Steps:
1. State problem (based on observations)
2. Observe and collect data (senses and instruments)
Data—recorded observations qualitative (descriptive) quantitative (numerical)
I. Scientific Method
Basic Steps:3. Form hypothesis (testable statement)4. Testing
a. Experimental setup (contains variable being tested)
b. Control (identical to experimental setup EXCEPT for the variable)
c. Ideally, only one variabled. Done multiple times (for consistency)
I. Scientific Method
Basic Steps:
5. Theorizing (conclusion)
a. hypotheses model theory
NOTE: Theories CANNOT turn into Laws
WHY?
I. Scientific Method
Basic Steps:Theory– attempts to explain WHY a set
of conditions produce a certain result
Law– states that a certain set of conditions will always produce a certain result but DOES NOT EXPLAIN WHY.
I. Scientific Method
Basic Steps:
Ex. Theory of Plate Tectonics
Ex. Law of Universal Gravitation
I. Scientific Method
Basic Steps:
A scientific theory makes falsifiable predictions about things not yet observed.
A “theory” that makes no predictions that will ever be observed is not a theory.
Predictions which are not sufficiently specific to be falsified are meaningless and likewise not a scientific theory.
II. Units of Measurements
Temperature Scales:
Water oF(Fahrenheit)
oC
(Celsius)
K
(Kelvin)
Boiling pt. 212 100 373.15
Freezing pt.
32 0 273.15
Absolute Zero
-459.67 -273.15 0
180 100 100
II. Units of Measurements
Temperature Scales: 180 oF = 100 oC = 100 K 1.8 oF = 1 oC = 1 K
II. Units of Measurements
Converting between Temperature Scales: K = oC + 273.15 oF = (oC x 9/5) + 32
NOTE: You solve for the variable on the LEFT SIDE (your given quantity goes on the right side. Rearrange equations using algebra if necessary.
II. Units of Measurements
Converting between Temperature Scales:
Ex. Normal body temperature of humans is often described as around 98.6 oF. Determine what this is on the Celsius and Kelvin scales.
II. Units of Measurements
Density: mass per unit volume
D = m / V
m = D x V
II. Units of Measurements
Density: Units: kg / m3 (gives VERY large numbers for
dense substances; good for gases) g / cm3
g / mL
II. Units of Measurements
Density:
NOTE: 1 cm3 = 1 mL1 cm3 is the volume occupied by a cube that
measures 1 cm on each side.
Denser objects will sink in less dense fluids.
II. Units of Measurements
Density:
Ex. An object is placed into a graduated cylinder with 35.3 mL of water. After the object sinks, the volume of the water rises to 46.8 mL. If the object’s density is 2.47 g/cm3, what is the mass of the object?
II. Units of Measurements
Density:
Ex. Why will a 10.0 gram ball of clay sink if placed into a tray of water, but float if the clay is flattened out into the shape of a boat? NOTE: The density of water is 1.00 g/mL.
IV. Metric Conversion
Kids Have Dropped over dead converting metrics
2.45 hg = g
K H D o d c m
START
END
245.
ILO
ECTA
EKA
eci
enti
illi
IV. Metric Conversion
Kids Have Dropped over dead converting metrics
8.3 mm = dam
K H D o d c m
STARTEND
0 0 0 .00083
IV. Metric Conversion
Kids Have Dropped over dead converting metrics
mega (M) = 106 micro () = 10-6
giga (G) = 109 nano (n) = 10-9
tera (T) = 1012 pico (p) = 10-12
T _ _ G _ _ M _ _ K H D o d c m _ _ _ _ n _ _ p
Video 2-2
Scientific Notation Significant Figures Math and Sigfigs Percent Error
VII. Scientific Notation
value is expressed in the form:
a.bbb x 10y
where a.bbb must be between 1 and 10
VII. Scientific Notation
Ex. Write the following in scientific notation:
5203.04 = 5.20304 x 103
0.000254= 2.54 x 10-4
102.56 x 102
= 1.0256 x 104
2.5498= 2.5498 x 100
VII. Scientific Notation
Use your calculator to convert standard notation into scientific notation
Look for the “sci” mode (varies with calculators)
VIII. Significant Figures
Significant figures: all the numbers in a measurement that can be known precisely plus a last digit that must be estimated.
All the numbers you are sure of plus one more decimal place (estimated).
VIII. Significant Figures
Rules for determining HOW MANY SIGFIGS in a measurement:
1) Count all nonzero digits (no matter is before or after decimal).
Ex. 584.39 g
2) Count all zeros between nonzero numbers.
Ex. 4300.002308 mL
VIII. Significant Figures
Rules for determining HOW MANY SIGFIGS in a measurement:
3) Do NOT count zeros in front of nonzero digits (place holders).
Ex. 0.000546902 kg
VIII. Significant Figures
Rules for determining HOW MANY SIGFIGS in a measurement:
4) Count zeros at the END of a number ONLY if the number contains a decimal point. If there is no decimal point, the zeros are UNCERTAIN.
Ex. 4950.87000 mm 678900 L
VIII. Significant Figures
Ex. Determine how many sigfigs are in each of the following measurements:
354.2 g 32.0305 mL 0.00254 km 0.34050 mm 235000 hL
46
3
5
?
VIII. Significant Figures
When rounding off a number to a specific number of sigfigs: Find the LAST sigfig in the number and look at
the number AFTER it. If it is 5 or greater, round the last sigfig up (ignore book rules). If it is less than five, drop all digits after the last sigfig.
NOTE: When converting a measurement to scientific notation, the number of sigfigs MUST be the same as in the original measurement.
VIII. Significant Figures
Ex. Round off the following numbers to the indicated number of sigfigs and rewrite the answer in scientific notation.
measurement No. of sigfigs Answer Scientific Notation
5247.23 g 5
96742.35 m 3
0.045038 L 1
24.85 x 106 g 2
5247.2 g 5.2472 x 103 g
96700 m 9.67 x 104 m
0.05 L 5 x 10-2 L
25 x 106 g 2.5 x 107 g
IX. Mathematical Operations with Sigfigs
Addition or Subtraction: The answer must have the same number of
DECIMAL PLACES as the measurement with the LEAST number of decimal places.
IX. Mathematical Operations with Sigfigs
Ex. Answer the following with the correct number of sigfigs:
563.02 + 12.027 =
1002.5 + 0.254831 =
500 – 6.842 + 24.51 =
575.047 = 575.05
1002.754831 = 1002.8
517.668 = 518
IX. Mathematical Operations with Sigfigs
Multiplication or Division: The answer cannot have more sigfigs than the
measurement with the LEAST total number of sigfigs.
IX. Mathematical Operations with Sigfigs
Ex. Answer the following with the correct number of sigfigs:
563.02 ÷ 12.02 =
10.05 x 0.254 =
508 ÷ 6.842 x 24.51 =
46.8402662 = 46.84
2.5527 = 2.55
1819.801228 = 1.82 x 103
IX. Mathematical Operations with Sigfigs
For all operations, perform ALL similar operations (+ and – are similar; x and are similar) FIRST, then round off to the proper number of sigfigs. Do NOT round off after each calculation
IX. Mathematical Operations with Sigfigs
Ex. Answer the following with the correct number of sigfigs:
563.02 x 12.02 / 21.3 =
10.05 + 0.254 – 6.2 =
317.7230235 = 318
4.104 = 4.1
IX. Mathematical Operations with Sigfigs
If there is a mixture of operations, round off before going to a “dissimilar” operation. Use the rules for the last operation you just did.
IX. Mathematical Operations with Sigfigs
Ex. Answer the following with the correct number of sigfigs:
(563.02 ÷ 12.02) + 3.2 = 46.8402662 + 3.2
= 46.84 + 3.2 = 50.04 = 50.0
IX. Mathematical Operations with Sigfigs
Ex. Answer the following with the correct number of sigfigs:
(563.02 + 12.8) x 3.2 / 5.408 =
575.82 x 3.2 / 5.408
= 340.7100592 = 340 = 3.4 x 102
= 575.8 x 3.2 / 5.408
X. Calculating Percent Error
Percent error
% error =
can have a positive or negative value Less than 5% error (for small values)
Valueaccepted - Valueexperimental
Valueaccepted X 100%
Video 2-3
Graphing Data and Numerical Relationships
XI. Graphing Data and Numerical Relationships
Directly proportional quantities: y/x = a constant y = kx where k is the slope straight line
XI. Graphing Data and Numerical Relationships
X
Y
..
..
..
. .
XI. Graphing Data and Numerical Relationships
Inversely proportional quantities: xy = a constant y = k/x hyperbola
XI. Graphing Data and Numerical Relationships
X
Y
.
.
..
. . .
XI. Graphing Data and Numerical Relationships
GRAPHING DATA: Often, you will have to graph data that you
measured. In experimental sciences, there are two types of variables:
XI. Graphing Data and Numerical Relationships
1. Independent variables—a variable that YOU can determine, manipulate, vary, control, etc.
2. Dependent variable—a variable that CHANGES (or is determined) by your actions or input.
XI. Graphing Data and Numerical Relationships
X-axis: independent axis (variable) Y-axis: dependent axis (variable) Graphing is ALWAYS the dependent vs. independent variable (y vs. x)
XI. Graphing Data and Numerical Relationships
Time (seconds)
Temperature (oC)
Temperature vs. Time
Video 2-4
Dimensional Analysis Derived Units Problem Solving Strategies
XII. Dimensional Analysis
When CONVERTING a measurement between one system of units to another, simply do this:
Given Quantity (units) Xunits getting rid of
new unitsnumber
number
XII. Dimensional Analysis
When CONVERTING a measurement between one system of units to another, simply do this:
Given Quantity (units) Xunits getting rid of
new unitsnumber
number
CONVERSION FACTOR
XII. Dimensional Analysis
Conversion factor is simply (and ALWAYS) a fraction that is equal to 1
Numerator is equivalent to the denominator Use EQUALITIES
XII. Dimensional Analysis
Examples:
1 ft = 12 inches 2.205 lbs = 1 kg1 hr = 3600 sec 1000 m = 1 km
NOTE: the 1 ft, 1 kg, 1 km, 1 hr in these equalities are EXACT (defining) quantities and have an INFINITE number of sigfigs (values are 1.000000000000000 . . .)
XII. Dimensional Analysis
Examples:
How many pounds are in 9.8 kg?
9.8 kg xkg
lbs2.205
1
= 21.609 lbs = 22 lbs
XII. Dimensional Analysis
Examples:
If 1 inch is equivalent to 2.54 cm, how many inches are in 2.50 m?
2.50 m xm
cm
1 inch = 2.54 cm
1
100x
cm
in
2.54
1
= 98.42519685 in = 98.4 in
III. Derived Units
units that are obtained by multiplying or dividing standard units: Ex. volume = length (m) x width (m) x height (m) V = m x m x m = m3
Finding equivalent units:
III. Derived Units
Finding equivalent units:
1 m3 = ? cm3
1 m = 100 cm
(1 m)3 = (100 cm)3
1 m3 = 1,000,000 cm3 = 1 x 106 cm3
III. Derived Units
Finding equivalent units:
Ex. How many square feet are equivalent to a square meter? 1 meter = 3.28 feet
XIII. Problem Solving Strategies
The problems facing you in this class will fall into one of the following categories:
1. Conversion (changing a measurement to a different unit)
2. Formula (changing one type of measurement to a different TYPE of measurement)
XIII. Problem Solving Strategies
Often, you will need to do both things. So, first, determine which formula you need to
use (rearrange the formula for the unknown)
second, convert any given quantities into the proper units if necessary
third, plug the values in and calculate
XIII. Problem Solving Strategies
What are some terms that mean: Equals Add Subtract Multiply Divide
Video 2-5
Measuring Techniques Accuracy and Precision
V. MEASURING TECHNIQUES
A measurement is a comparison against a STANDARD UNIT.
3 Standard types of measurements: Mass (the amount of matter present in
something) Volume (the amount of space something takes
up) Length (the distance from one part of the object
to another part)
V. MEASURING TECHNIQUES
Standard units (Metric System)
Length: Meter (millimeter, centimeter, kilometer)
Volume: Liter (milliliter, cubic centimeter) Mass: Kilogram (gram, milligram)
V. MEASURING TECHNIQUES
MAKING MEASUREMENTS:
1) Determine the value of the SMALLEST unit (line) that the instrument will measure.
V. MEASURING TECHNIQUES
Meter stick (ruler):
1 line = 1 millimeter = 0.1 centimeters
V. MEASURING TECHNIQUES
Electronic Balance (mass):
No lines (digital display)
V. MEASURING TECHNIQUES
Graduated cylinder (volume): varies with capacity of the cylinder
V. MEASURING TECHNIQUES
2) Use proper techniques for measuring: Rulers: Do NOT start measuring from the
beginning of the ruler. Start from the 1 centimeter (10 millimeter) mark. SUBTRACT 1 cm (or 10 mm) from your measurement.
V. MEASURING TECHNIQUES
V. MEASURING TECHNIQUES
2) Use proper techniques for measuring: Balance: Record reading after it has
stabilized (check and include units)
V. MEASURING TECHNIQUES
2) Use proper techniques for measuring: Graduated cylinder: Make sure the
meniscus (curve of fluid) is at eye level. Read the BOTTOM of the meniscus.
V. MEASURING TECHNIQUES
3) Estimating decimal places. Make sure you ESTIMATE one more
decimal place to the right. If the instrument reads to the 0.1, estimate to the 0.01 place.
V. MEASURING TECHNIQUES
3) Estimating decimal places.
V. MEASURING TECHNIQUES
3) Estimating decimal places.
V. MEASURING TECHNIQUES
4) Filling a cylinder to a specific volume. Use a beaker and dropper to fill a
GRADUATED CYLINDER.
V. MEASURING TECHNIQUES
5) Electronic Balance: Tare (or Zero) button will set reading
to 0.00 g (ignores any mass on balance)
Do NOT estimate an extra decimal place (last digit is already an estimate).
V. MEASURING TECHNIQUES
5) Electronic Balance:
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Beaker?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Beaker? Holding liquid (easy to pour) Mixing liquid with stirring rod Heating liquid NOT for measuring volume
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Erlenmeyer flask?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Erlenmeyer flask? Mixing (swirling) liquid Heating liquid NOT for pouring NOT for measuring volume
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Graduated cylinder?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Graduated cylinder? Measuring volumes accurately NOT for heating NOT for storing large quantities
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Pipet?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Pipet? TRANSFERRING a precise amount of
liquid
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Buret?
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
When should you use a Buret? When you DON’T know how much of a
liquid you will need Transferring precise amounts of liquid.
V. MEASURING TECHNIQUES
6) Choosing the correct piece of lab equipment:
What size should you use?
Smallest size possible that will “get the job done” (measure quantities without being refilled).
VI. Accuracy and Precision
Accuracy: the closeness of measurements to the correct or accepted value of the measured quantity.
Precision: the reproducibility of a set of measurements made in the same way.
Significant figures (sigfigs) reflect the precision of a measurement.
VI. Accuracy and Precision
Neither accurate nor precise
VI. Accuracy and Precision
Precise
VI. Accuracy and Precision
Both accurate and precise
VI. Accuracy and Precision
Examples: One students measures the length of an
object to be 10.2 cm. The actual length is 10.8 cm. Is his measurement accurate? Precise?
VI. Accuracy and Precision
Examples: One students measures the length of an
object to be 10.2 cm. The actual length is 10.8 cm. Is his measurement accurate? Precise?
% error = (10.8 – 10.2) / 10.8 x 100
= 5.56 %
VI. Accuracy and Precision
Examples: One students measures the length of an
object to be 10.2 cm. The actual length is 10.8 cm. Is his measurement accurate? Precise?
To determine if it is precise, more measurements are needed.
VI. Accuracy and Precision
Examples: One students measures the length of an
object to be 10.2 cm. The actual length is 10.8 cm. Is his measurement accurate? Precise?
He measures it 3 more times. Values are 10.7 cm, 11.4 cm, and 10.9 cm.
VI. Accuracy and Precision
Examples: One students measures the length of an
object to be 10.2 cm. The actual length is 10.8 cm. Is his measurement accurate? Precise?
NOT precise. But, the average of his 4 measurements is 10.8 cm.
Improved ACCURACY
VI. Accuracy and Precision
Why is his precision poor? What do the markings on his ruler look like? Remember the rules for measuring
One more decimal place than the ruler can read to.
Ruler’s smallest marking are 1 cm
VI. Accuracy and Precision
Why is his precision poor? If the marking are worth 0.1 cm he can
better estimate the measurement (sure of the 0.1 cm, estimate the 0.01 cm place).
Measurements should be REPRODUCIBLE to the 0.1 cm
Does NOT mean they will be accurate