What is measurement? Units of

Measurement When do you

Measure?• measure your height. • read your watch.• take your temperature.

• weigh a cantaloupe.

1

2

Measurement in ChemistryIn chemistry we

• measure quantities.• do experiments.• calculate results. • use numbers to report

measurements.• compare results to

standards.• all with needed tools• every measurement,

• number followed by unit

Number and Unit

35 m

0.25 L

225 lb

3.4 hr

The Metric System (SI)

metric system or SI (international system)

• decimal system based on 10.

• Used worldwide.(M)

• Used by scientists (SI).

following unit used for each type of measurement:

Measurement Metric SILength

meter (m) meter (m)Volume

liter (L) cubic meter (m3)Mass

gram (g) kilogram (kg)Time

second (s) second (s)Temperature

Celsius (C) Kelvin (K)

4

Length Measurement

Length

• measured using a meter stick.

• Uses unit of meter (m) in both systems.

• unit of an inch equal to exactly 2.54 centimeters in metric (SI) system.

1 in. = 2.54 cm

5

Volume Measurement

Volume • space occupied by a

substance. • measured using a

graduated cylinder (liquids)

• metric system• unit liter (L) in• 1 L = 1.057 qt

• SI system (solids)• m3(cubic meter)

Mass Measurement

mass of an object

• quantity of material it contains.

• measured • balance.

• metric system• . gram (g)

• SI system• kilogram (kg)

Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings

7

Temperature Measurement

temperature of a substance • indicates how hot or cold.• metric system

• Celsius (C)

• SI system • Kelvin (K) scale.

• thermometer here shows• 18ºC or 64ºF.

8

Time Measurement

Time measurement

• metric and SI systems.• second(s)

• based on an atomic clock • uses a frequency

emitted by cesium atoms

What are scientific notation?• very large or very small numbers

• coefficient and a power of 10• width human hair is 0.000 008 m

• written 8 x 10-6 m.• large number such as 4 500 000 s

• written 4.5 x 106 s

• Let’s explore more ! coefficient power of ten coefficient

power of ten 1.5 x 102 7.35 x

10-4

decimal point moved after first digit

spaces moved shown as power of ten. 52 000. = 5.2 x 10 4 0.00378 = 3.78 x

10-3

4 spaces left 3 spaces right

Some Powers of Ten

Numbers written in standard format

and in scientific notation.

Diameter of the Earth12 800 000 m

1.28 x 107 m Mass of a human

68 kg 6.8 x 101 kg

Length of a pox virus0.000 03 cm

3 x 10-5 cm10

. l2. . . . l . . . . l3 . . . . l . . . . l4. . cm

• determine a quantity such as height or mass• markings on meter stick end of orange line are read

asfirst digit 2 plus second digit 2.7

• last digit obtained by estimating• length reported as 2.76 cmdigits 2 and 7 are certain

(known).• The final digit 6 was estimated (uncertain).• All three digits (2.76) are significant including

estimated digit.

What are measured numbers ?

. l3. . . . l . . . . l4. . . . l . . . . l5. . cm

• For this measurement• first and second known digits are 4.5.

• line ends on mark• estimated digit in hundredths place 0.

• measurement • reported as 4.50 cm.

Zero as a Measured Number!

What are significant numbers?Significant figures • obtained from

measurement• include all known

digits plus estimated digit.

• reported • measurement depend on

measuring tool.

• non-zero numbers in measured number are significant.

13

38.15 cm 45.6 ft 265.6 lb

3122.55 m 5

The two kinds of zeros?

Sandwiched zeros• occur between nonzero

numbers.• are significant.

Number significant digits

50.8 mm 32001 min 4 0.0702 lb 3 0.40505 m 5

Trailing zeros & Leading zeros

• follow non-zero numbers in numbers without decimal points.

• Precede non-zero digits in a decimal number

• are usually place holders. • are not significant.

Number significant digits

25 000 cm 2 200 kg 10.0156 oz 30.0042 lb 225 005 000 g 5

What are prefixes?

A prefixfront of a unit increases or decreases size makes units larger or smaller

one or more factors of 10. indicates a numerical value.

prefix = value1 kilometer = 1000 meters

1 kilogram = 1000 grams

16

Metric and SI Prefixes need to know!

An equality

states same measurement in two different units.can be written using

relationships between two metric units.

Example: 1 meter same as 100 cm and 1000 mm.

1 m = 100 cm1 m = 1000 mm

What are metric equalities?

Measuring Length

Several equalities can be written for length metric (SI) system

1 km = 1000 m

1 m = 1000 mm

1 m = 100 cm

1 mm = 0.001 m

19

Measuring Volume

Several equalities can bewritten for volume metric(SI) system

1 kl = 1000 l1 l = 1000 ml1 l = 100 cl1 ml = 0.001 l

20

Measuring Mass

Several equalities can be

written for mass metric (SI) system

1 kg = 1000 g1 g = 1000 mg1 g = 100 cg

1 mg = 0.001 g

Equalities • use two different units

• Describe same measured amount.

• written for relationships between units of the metric system, U.S. units, or between

For example,

1 m = 1000 mm

1 lb = 16 oz

2.205 lb = 1 kg

Other equalities between metric and U.S. units?

22

Some Common Equalities

contents of packaged foods

• U.S. are listed as both metric and U.S. units• Indicate same amount of a substance in two

different units.

A conversion factor • fraction obtained from an equality

Equality: 1 in. = 2.54 cm• written as a ratio with a numerator and

denominator.

• can be inverted to give two conversion factors for every equality. 1 in. and 2.54 cm

2.54 cm 1 in.

Use conversion factors to change between units!

A conversion factor • may be obtained from information in a word

problem.• written for that problem only.

Example 1: The price of one pound (1 lb) of red peppers is

$2.39.1 lb red peppers and $2.39$2.39 1 lb red peppers

Example 2: The cost of one gallon (1 gal) of gas is $2.34.

1 gallon of gas and $2.34$2.34 1 gallon of gas

Conversion Factors in a Problem

A percent factor• Gives ratio of the parts to whole.

% = Parts x 100Whole

• Uses same unit to express percent.• Uses value 100 and unit for whole.• can be written as two factors.

Example: A food contains 30% (by mass) fat.

30 g fat and 100 g food100 g food 30 g fat

Percent as a Conversion Factor

26

The thickness of the skin fold at

the waist indicates 11% body

fat. What percent factors can be

written for body fat in kg?

Percent factors using kg:

11 kg fat and 100 kg mass

100 kg mass 11 kg fat

Another example!

To solve a problem• Identify given unit• Identify needed unit.

Example: A person has a height of 2.0 meters. What is that height in inches?

given unit is initial unit of height. given unit = meters (m)

needed unit is unit for answer. needed unit = inches (in.)

Given and Needed Units can be used in problem solving!

Learning Check

An injured person loses 0.30 pints of blood. How

many milliliters of blood would that be?

Identify the given and needed units given in this

problem.

Given unit = _______

Needed unit = _______

1. Write given and needed units.2. Write a unit plan to convert given unit to needed

unit.3. Write equalities and conversion factors to

connect units.4. Use conversion factors to cancel given unit and

provide needed unit.

Unit 1 x Unit 2 = Unit 2

Unit 1Given x Conversion = Needed

unit factor unit

Problem Setup steps!

30

How many minutes are 2.5 hours?

Given unit = 2.5 hrNeeded unit = minUnit Plan = hr

min

Setup problem to cancel hours (hr).

Given Conversion Neededunit factor unit2.5 hr x 60 min = 150 min

(2 SF) 1 hr

Setting up a Problem

Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings

A rattlesnake is 2.44 m long. How many centimeters long is the snake?

Given Conversion Neededunit factor unit

2.44 m x 100 cm = 244 cm 1 m

A solved example

• Often, two or more conversion factors are required to obtain unit needed for answer.Unit 1 Unit 2Unit 3

• Additional conversion factors are placed in setup to cancel each preceding unit

Given unit x factor 1 x factor 2 = needed unitUnit 1 x Unit 2 x Unit 3 = Unit 3

Unit 1 Unit 2

Using Two or More Factors

How many minutes are in 1.4 days? Given unit: 1.4 days

Factor 1 Factor 2 Plan: days hr min

Set up problem: 1.4 days x 24 hr x 60 min = 2.0 x 103 min

1 day 1 hr 2 SF Exact Exact = 2 SF

Example: Problem Solving

• check your unit cancellation in setup.• units in conversion factors must cancel to give

correct unit for answer.

What is wrong with the following setup?

1.4 day x 1 day x 1 hr 24 hr 60 min

Units = day2/min is not the unit neededUnits don’t cancel properly.

Remember to check the unit cancellation!

Another example! the GPS

What is 165 lb in kg?STEP 1 Given 165 lb Need

kgSTEP 2 PlanSTEP 3 Equalities/Factors 1 kg = 2.20 lb 2.20 lb and 1 kg

1 kg 2.20 lbSTEP 4 Set Up Problem 165 lb x 1 kg = 75.0

kg 2.20 lb

Given: 4.65 L Needed: gallons

Plan: L qt gallon

Equalities: 1.06 qt = 1 L; 1 gal = 4 qt

Set Up Problem:

4.65 L x x 1.06 qt x 1 gal = 1.23 gal 1 L 4 qt

3 SF 3 SF exact 3 SF

A bucket contains 4.65 L of water. How many gallons of water is that?

3.0 ft x 12 in x 2.54 cm x 10 mm = 1 ft 1 in. 1 cm

Calculator answer: 914.4 mm Needed answer: 910 mm (2 SF rounded)

Check factor setup: Units cancel properlyCheck needed unit: mm

If a ski pole is 3.0 feet in length, how long is the ski pole in mm?

If your pace on a treadmill is 65 meters per minute, how many minutes will it take for you to walk a distance of 7500 feet?

Given: 7500 ft 65 m/min Need: min

Plan: ft in. cm m min

Equalities: 1 ft = 12 in. 1 in. = 2.54 cm 1 m = 100 cm

1 min = 65 m (walking pace)

Set Up Problem:

7500 ft x 12 in. x 2.54 cm x 1m x 1 min 1 ft 1 in. 100 cm 65 m

= 35 min final answer (2 SF)

39

Percent Factor in a Problem

Copyright © 2005 by Pearson Education, Inc.Publishing as Benjamin Cummings

If the thickness of the skin fold at the waist indicates an 11% body fat, how much fat is in a person with a mass of 86 kg?

percent factor

86 kg mass x 11 kg fat

100 kg mass

= 9.5 kg fat

Another example:

How many lb of sugar are in 120 g of candy if the candy is 25%(by mass) sugar?

percent factor

120 g candy x 1 lb candy x 25 lb sugar

454 g candy 100 lb candy

= 0.066 lb sugar

Density• Compares the mass of an object to its

volume.• Is the mass of a substance divided by its

volume.

Density expressionDensity = mass = g or g = g/cm3 volume mL cm3

Note: 1 mL = 1 cm3

• Ice floats in water • because density of ice is less than density of

water.

• Aluminum sinks • because its density is greater than density of

water

What is density?

Osmium is a very dense metal. What is its density in g/cm3 if 50.0 g of osmium has a volume of 2.22 cm3?

Given: mass = 50.0 g volume = 22.2 cm3

Plan: Place the mass and volume of the osmium metal

in the density expression.

D = mass = 50.0 g volume 2.22 cm3

calculator = 22.522522 g/cm3

final answer (2) = 22.5 g/cm3

Problem on density

43

How to determine volume by displacement ?

• solid completely submerged in water displaces its own volume of water.

• volume of solid is calculated from volume difference.45.0 mL - 35.5 mL

= 9.5 mL = 9.5 cm3

44

Density Using Volume Displacement

The density of the zinc object is

then calculated from its mass

and volume.

mass = 68.60 g = 7.2 g/cm3 volume 9.5 cm3

What is the density (g/cm3) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added?

Find the volume first?

object

33.0 mL 25.0 mL

Solution

Given: 48.0 g Volume of water = 25.0 mL

Volume of water + metal = 33.0 mL

Need: Density (g/mL)Plan: Calculate the volume difference. Change to

cm3, and place in density expression.

33.0 mL - 25.0 mL = 8.0 mL

8.0 mL x 1 cm3 = 8.0 cm3

1 mLSet up Problem:

Density = 48.0 g = 6.0 g = 6.0 g/cm3

8.0 cm3 1 cm3