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1
Chapter 1 Measurements
1.1 Units of Measurement
Copyright © 2009 by Pearson Education, Inc.
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Measurement
You make a measurementevery time you
• measure your height. • read your watch.• take your temperature.• weigh a cantaloupe.
Copyright © 2009 by Pearson Education, Inc.
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Measurement in Chemistry
In chemistry we
• measure quantities.• do experiments.• calculate results. • use numbers to report
measurements.• compare results to
standards.Copyright © 2009 by Pearson Education, Inc.
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Measurement
In a measurement
• a measuring tool is used to compare some dimension of an object to a standard.
• of the thickness of the skin fold at the waist, calipers are used. Copyright © 2009 by Pearson Education, Inc.
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Stating a Measurement
In every measurement, a number is followed by a unit.
Observe the following examples of measurements:
Number and Unit 35 m 0.25 L 225 lb 3.4 kg
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The Metric System (SI)
The metric system or SI (international system) is
• a decimal system based on 10.
• used in most of the world.
• used everywhere by scientists.
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Units in the Metric System
In the metric and SI systems, one unit is used for each type of measurement:
Measurement MetricSILength 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)
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Length Measurement
Length • is measured using a
meterstick.
• uses the unit of meter (m) in both the metric and SI systems.
Copyright © 2009 by Pearson Education, Inc.
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Inches and Centimeters
The unit of an inch is equal to exactly 2.54 centimeters in the metric (SI) system.
1 in. = 2.54 cm
Copyright © 2009 by Pearson Education, Inc.
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Volume Measurement
Volume • is the space occupied by a
substance.
• uses the unit liter (L) in the metric system.
• 1 qt = 946 mL
• uses the unit m3 (cubic meter) in the SI system.
• is measured using a graduated cylinder.
Copyright © 2009 by Pearson Education, Inc.
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Mass Measurement
The mass of an object
• is the quantity of material it contains.
• is measured on a balance.• uses the unit gram (g) in the
metric system.• uses the unit kilogram (kg) in
the SI system.
Copyright © 2009 by Pearson Education, Inc.
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Temperature Measurement
The temperature of a substance • indicates how hot or cold it is.• is measured on the Celsius
(C) scale in the metric system.
• on this thermometer is 18 ºC or 64 ºF.
• in the SI system uses the Kelvin (K) scale.
Copyright © 2009 by Pearson Education, Inc.
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Time Measurement
Time measurement
• uses the unit second (s) in both the metric and SI systems.
• is based on an atomic clock that uses the frequency of cesium atoms.
Copyright © 2009 by Pearson Education, Inc.
Summary of Units of Measurement
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For each of the following, indicate whether the unit describes 1) length, 2) mass, or 3) volume.
____ A. A bag of tomatoes is 4.6 kg.
____ B. A person is 2.0 m tall.
____ C. A medication contains 0.50 g aspirin.
____ D. A bottle contains 1.5 L of water.
Learning Check
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Learning Check
Identify the measurement that has an SI unit. A. John’s height is
1) 1.5 yd. 2) 6 ft . 3) 2.1 m.
B. The race was won in1) 19.6 s. 2) 14.2 min. 3) 3.5 h.
C. The mass of a lemon is1) 12 oz. 2) 0.145 kg. 3) 0.6 lb.
D. The temperature is1) 85 C. 2) 255 K. 3) 45 F.
Measurements
1.2Scientific Notation
Copyright © 2009 by Pearson Education, Inc.
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Scientific Notation
Scientific Notation
• is used to write very large or very small numbers.
• for the width of a human hair of 0.000 008 m is written 8 x 10-6 m.
• of a large number such as 4 500 000 s is written 4.5 x 106 s. Copyright © 2009 by Pearson Education, Inc.
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Numbers in Scientific Notation
A number written in scientific notation contains a• coefficient.• power of 10.
Examples:
coefficient power of ten coefficient power of ten 1.5 x 102 7.35 x 10-4
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Writing Numbers in Scientific Notation
To write a number in scientific notation,
• move the decimal point to give a number 1-9.
• show the spaces moved as a power of 10.Examples: 52 000. = 5.2 x 10
4 0.00178 = 1.78 x 10-3
4 spaces left 3 spaces right
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Some Powers of 10
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Comparing Numbers in Standard and Scientific Notation
Here are some numbers written in standard format and in scientific notation.
Number in Number in Standard Format Scientific Notation
Diameter of the Earth12 800 000 m 1.28 x 107 m
Mass of a typical human68 kg 6.8 x 101 kg
Length of a pox virus0.000 03 cm 3 x 10-5 cm
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Study Tip: Scientific Notation
In a number 10 or larger, the decimal point • is moved to the left to give a positive power of 10
In a number less than 1, the decimal point • is moved to the right to give a negative power of 10
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Learning Check
Select the correct scientific notation for each.
A. 0.000 008 m1) 8 x 106 m, 2) 8 x 10-6 m, 3) 0.8 x 10-5 m
B. 72 000 g1) 7.2 x 104 g, 2) 72 x 103 g, 3) 7.2 x 10-4 g
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Learning Check
Write each as a standard number.
A. 2.0 x 10-2 L 1) 200 L, 2) 0.0020 L, 3) 0.020 L
B. 1.8 x 105 g 1) 180 000 g, 2) 0.000 018 g, 3) 18 000 g
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1.3Measured Numbers and
Significant Figures
Chapter 1 Measurements
Copyright © 2009 by Pearson Education, Inc.
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Measured Numbers
A measuring tool
• is used to determine a quantity such as height or the mass of an object.
• provides numbers for a measurement called measured numbers. Copyright © 2009 by Pearson Education, Inc.
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. l2. . . . l . . . . l3 . . . . l . . . . l4. . cm
• The markings on the meterstick at the end of the orange line are read as:
the first digit 2
plus the second digit 2.7 • The last digit is obtained by estimating. • The end of the line may be estimated between 2.7–
2.8 as half way (0.5) or a little more (0.6), which gives a reported length of 2.75 cm or 2.76 cm.
Reading a Meterstick
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Known & Estimated Digits
If the length is reported as 2.76 cm,
• the digits 2 and 7 are certain (known).• the final digit, 6, is estimated (uncertain).• all three digits (2, 7, and 6) are significant, including
the estimated digit.
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. l8. . . . l . . . . l9. . . . l . . . . l10. . cm
What is the length of the orange line?
1) 9.0 cm
2) 9.04 cm
3) 9.05 cm
Learning Check
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. l3. . . . l . . . . l4. . . . l . . . . l5. . cm
• For this measurement, the first and second known digits are 4 and 5.
• When a measurement ends on a mark, the estimated digit in the hundredths place is 0.
• This measurement is reported as 4.50 cm.
Zero as a Measured Number
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Significant Figures in Measured Numbers
Significant Figures
• obtained from a measurement include all of the known digits plus the estimated digit.
• reported in a measurement depend on the measuring tool.
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Significant Figures
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All nonzero numbers in a measured number are significant.
Number of Measurement Significant Figures38.15 cm 45.6 ft 265.6 lb 3122.55 m 5
Counting Significant Figures
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Sandwiched Zeros• occur between nonzero numbers.• are significant.
Number of Measurement Significant Figures50.8 mm 32001 min 40.0702 lb 30.405 05 m 5
Sandwiched Zeros
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Trailing Zeros• follow nonzero numbers in numbers without
decimal points.• are usually placeholders. • are not significant.
Number of Measurement Significant Figures25 000 cm 2
200 kg 1 48 600 mL 3
25 005 000 g 5
Trailing Zeros
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Leading Zeros • precede nonzero digits in a decimal number. • are not significant.
Number of Measurement Significant Figures0.008 mm 10.0156 oz 30.0042 lb 20.000 262 mL 3
Leading Zeros
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State the number of significant figures in each of the following measurements.
A. 0.030 mB. 4.050 LC. 0.0008 g D. 2.80 m
Learning Check
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Significant Figures in Scientific Notation In scientific notation all digits in the coefficient including zeros are significant.
Number of Measurement Significant Figures8 x 104 m 18.0 x 104 m 28.00 x 104 m 3
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Study Tip: Significant Figures
The significant figures in a measured number are• all the nonzero numbers.
12.56 m 4 significant figures• zeros between nonzero numbers.
4.05 g 3 significant figures• zeros that follow nonzero numbers in a decimal number.
25.800 L 5 significant figures
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A. Which answer(s) contain 3 significant figures? 1) 0.4760 2) 0.00476 3) 4.76 x 103
B. All the zeros are significant in 1) 0.00307. 2) 25.300. 3) 2.050 x 103.
C. The number of significant figures in 5.80 x 102 is 1) one (1). 2) two (2). 3) three (3).
Learning Check
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In which set(s) do both numbers contain the same number of significant figures?
1) 22.0 and 22.00
2) 400.0 and 40
3) 0.000 015 and 150 000
Learning Check
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Examples of Exact Numbers
An exact number is obtained
• when objects are counted. Counted objects
2 soccer balls4 pizzas
• from numbers in a defined relationship. Defined relationships
1 foot = 12 inches1 meter = 100 cm
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Exact Numbers
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Learning Check
A. Exact numbers are obtained by 1. using a measuring tool.
2. counting.3. definition.
B. Measured numbers are obtained by 1. using a measuring tool.
2. counting.3. definition.
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Learning Check
Classify each of the following as (1) exact or (2) measurednumbers.
A.__Gold melts at 1064 °C.
B.__1 yard = 3 feet
C.__The diameter of a red blood cell is 6 x 10-4 cm.
D.__There are 6 hats on the shelf.
E.__A can of soda contains 355 mL of soda.
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Chapter 1 Measurements
1.4Significant Figures in
Calculations
Copyright © 2009 by Pearson Education, Inc.
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Rounding Off Calculated Answers
In calculations,• answers must have the same
number of significant figures as the measured numbers.
• a calculator answer often must be rounded off.
• rounding rules are used to obtain the correct number of significant figures.
Copyright © 2009 by Pearson Education, Inc.
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Rounding Off Calculated Answers
When the first digit dropped is 4 or less, • the retained numbers remain the same.
45.832 rounded to 3 significant figuresdrops the digits 32 = 45.8
When the first digit dropped is 5 or greater, • the last retained digit is increased by 1.
2.4884 rounded to 2 significant figuresdrops the digits 884 = 2.5 (increase by
0.1)
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Adding Significant Zeros
• Sometimes a calculated answer requires more significant digits. Then, one or more zeros are added.
Calculated Zeros Added to Answer Give 3 Significant Figures
4 4.001.5 1.500.2 0.200
12 12.0
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Learning Check
Round off or add zeros to the following calculated answers to give three significant figures.
A. 824.75 cm
B. 0.112486 g
C. 8.2 L
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Calculations with Measured Numbers
In calculations with measured numbers, significant figures ordecimal places arecounted to determinethe number of figures inthe final answer.
Copyright © 2009 by Pearson Education, Inc.
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When multiplying or dividing • the final answer must have the same number of
significant figures as the measurement with the fewest significant figures.
• use rounding rules to obtain the correct number of significant figures.
Example:
110.5 x 0.048 = 5.304 = 5.3 (rounded)
4 SF 2 SF calculator 2 SF
Multiplication and Division
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Select the answer with the correct number of significant figures.
A. 2.19 x 4.2 = 1) 9 2) 9.2 3) 9.198
B. 4.311 ÷ 0.07 = 1) 61.59 2) 62 3) 60
C. 2.54 x 0.0028 = 0.0105 x 0.060
1) 11.3 2) 11 3) 0.041
Learning Check
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When adding or subtracting• the final answer must have the same number of
decimal places as the measurement with the fewest decimal places.
• use rounding rules to adjust the number of digits in the answer.
25.2 one decimal place + 1.34 two decimal places
26.54 calculated answer 26.5 final answer with one decimal place
Addition and Subtraction
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For each calculation, round off the calculated answer to give a final answer with the correct number of significant figures.
A. 235.05 + 19.6 + 2 = 1) 257 2) 256.7 3) 256.65
B. 58.925 - 18.2 =1) 40.725 2) 40.73 3) 40.7
Learning Check
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Chapter 1 Measurements
1.5Prefixes and Equalities
Copyright © 2009 by Pearson Education, Inc.
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Prefixes
A prefixl in front of a unit increases or decreases the size of that unit. l makes units larger or smaller than the initial unit by one or more
factors of 10. l indicates a numerical value.
prefix = value1 kilometer = 1000 meters1 kilogram = 1000 grams
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Metric and SI Prefixes
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Indicate the unit that matches the description.
1. A mass that is 1000 times greater than 1 gram. 1) kilogram 2) milligram 3) megagram
2. A length that is 1/100 of 1 meter. 1) decimeter 2) centimeter 3) millimeter
3. A unit of time that is 1/1000 of a second. 1) nanosecond 2) microsecond 3) millisecond
Learning Check
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Select the unit you would use to measure A. your height.
1) millimeters 2) meters 3) kilometers
B. your mass. 1) milligrams2) grams 3) kilograms
C. the distance between two cities. 1) millimeters 2) meters 3) kilometers
D. the width of an artery. 1) millimeters 2) meters 3) kilometers
Learning Check
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An equality
l states the same measurement in two different units.l can be written using the relationships between two metric
units.
Example: 1 meter is the same as 100 cm and 1000 mm. 1 m = 100 cm
1 m = 1000 mm
Metric Equalities
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Measuring Length
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Measuring Volume
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Measuring Mass
l Several equalities can be written for mass in the metric (SI) system
1 kg = 1000 g1 g = 1000 mg1 mg = 0.001 g1 mg = 1000 µg
Copyright © 2009 by Pearson Education, Inc.
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Indicate the unit that completes each of the followingequalities.
A. 1000 m = ___ 1) 1 mm 2) 1 km 2) 1 dm
B. 0.001 g = ___ 1) 1 mg 2) 1 kg 2) 1 dg
C. 0.1 s = ___ 1) 1 ms 2) 1 cs 2) 1 ds
D. 0.01 m = ___1) 1 mm 2) 1 cm 2) 1 dm
Learning Check
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Complete each of the following equalities.
A. 1 kg = ___ 1) 10 g 2) 100 g 3) 1000 g
B. 1 mm = ___ 1) 0.001 m 2) 0.01 m 3) 0.1 m
Learning Check