1. Chapter 1 Measurements 1.1 Units of Measurement
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2. Measurement in Chemistry
In chemistry we:
measure quantities.
do experiments.
calculate results.
use numbers to report measurements.
compare results to standards.

3. Stating a Measurement
In every measurement, a number is followed by a unit.
Observe the following examples of measurements:
Number and Unit m L lb hr

4. The Metric System (SI)
Metric units or the International System of Units (abbreviated SI units, from the French System International d’Unites)
a decimal system based on 10.
used in most of the world.
used everywhere by scientists.

5. Units in the Metric System
In the metric and SI systems, one unit is used for each type of measurement:
Measurement Metric SI
Length 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)

6. Length Length is measured using a meter stick.
uses the unit of meter (m) in both the metric and SI systems.
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7. 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
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8. Volume Volume is the space occupied by a substance.
uses the unit liter (L) or milliliter (mL).
1 L = 1000 mL
is m3(cubic meter) in the SI system.
is measured using a graduated cylinder.
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9. Mass 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.
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10. 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 18ºC or 64ºF.
in the SI system uses the Kelvin (K) scale.
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11. Time Measurement Time measurement
uses the unit second(s) in both the metric and SI systems.
is based on an atomic clock that uses a frequency emitted by cesium atoms.
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12. Scientific Notation Scientific notation
is used to write very large or very small numbers.
for the width of a human hair of m is written 8 x 10-6 m.
of a large number such as s is written 4.5 x 106 s.
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13. Writing Numbers in Scientific Notation
A number in scientific notation contains a coefficient and a power of 10.
coefficient power of ten coefficient power of ten
x x
To write a number in scientific notation, the decimal point is moved after the first digit.
The spaces moved are shown as a power of ten.
= x = x 10-3
4 spaces left spaces right

14. Some Powers of Ten

15. 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 Earth
m x 107 m
Mass of a human
68 kg x 101 kg
Length of a pox virus
cm x 10-5 cm

16. Practice Problems

17. Learning Check 1
For each of the following, indicate whether the unit describes length, mass, or volume and circle the units
____ 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.

18. Learning Check 2 Identify the measurement that has an SI unit.
A. John’s height is
1) 1.5 yd. 2) 6 ft ) 2.1 m.
B. The race was won in
1) s. 2) min ) 3.5 hr.
C. The mass of a lemon is
1) 12 oz. 2) kg ) 0.6 lb.
D. The temperature is
1) 85C. 2) 255 K ) 45F.

19. Solution 2 A. John’s height is 3) 2.1 m. B. The race was won in
C. The mass of a lemon is
2) kg.
D. The temperature is
2) 255 K.

20. Learning Check 3 Select the correct scientific notation for each.
1) 8 x 106 2) 8 x ) 0.8 x 10-5 B
1) 7.2 x 104 2) 72 x 103 3) 7.2 x 10-4

21. Solution 3 Select the correct scientific notation for each.
2) 8 x 10-6 B
1) 7.2 x 104

22. Learning Check 4 Write each as a standard number. A. 2.0 x 10-2
1) ) ) 0.020
B x 105
1) ) )

23. Solution 4 Write each as a standard number. A. 2.0 x 10-2 3) 0.0203)
B x 105 1)

24. Measured Numbers &
Significant Figures

25. 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.

26. Reading a Meter Stick
. l l l l l cm
The markings on the meter stick at the end of the orange line are read as
the first digit
plus the second digit 2.7
The last digit is obtained by estimating.
The end of the line might 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.

27. Known & Estimated Digits
In the length reported as 2.76 cm,
The digits 2 and 7 are certain (known).
The final digit 6 was estimated (uncertain).
All three digits (2.76) are significant including the estimated digit.

28. Zero as a Measured Number
. l l l l l5. . cm
For this measurement, the first and second known digits are 4.5.
Because the line ends on a mark, the estimated digit in the hundredths place is 0.
This measurement is reported as 4.50 cm.

29. Significant Figures in Measured Numbers
obtained from a measurement include all of the known digits plus the estimated digit.
reported in a measurement depend on the measuring tool.

30. Significant Figures

31. Counting Significant Figures
All non-zero numbers in a measured number are significant.
Number of
Measurement Significant Figures
38.15 cm
5.6 ft
65.6 lb m

32. Sandwiched Zeros Sandwiched zeros occur between nonzero numbers.
are significant.
Number of
Measurement Significant Figures
50.8 mm
2001 min lb m

33. Trailing Zeros Trailing zeros
follow non-zero numbers in numbers without decimal points.
are usually place holders.
are not significant.
Number of
Measurement Significant Figures cm
200 kg mL g

34. Leading Zeros Leading zeros
precede non-zero digits in a decimal number.
are not significant.
Number of
Measurement Significant Figures
0.008 mm oz lb mL

35. Significant Figures in Scientific Notation
In scientific notation all digits including zeros in the coefficient are significant.
Number of
Measurement Significant Figures
8 x 104 m
8.0 x 104 m
8.00 x 104 m

36. Examples of Exact Numbers
An exact number is obtained
when objects are counted.
Counted objects
2 soccer balls
4 pizzas
from numbers in a defined relationship.
Defined relationships
1 foot = 12 inches
1 meter = 100 cm

37. Exact Numbers

38. Scientific Notation The number of atoms in 12 g of carbon:
602,200,000,000,000,000,000,000
6.022 x 1023
The mass of a single carbon atom in grams:
1.99 x 10-23
N x 10n
N is a number
between 1 and 10
n is a positive or
negative integer
1.8

39. Addition & Subtraction w/ Scientific Notation
move decimal right
move decimal left
n > 0
n < 0
= x 102
= 7.72 x 10-6
Addition or Subtraction
Write each quantity with the same exponent n
Combine N1 and N2
The exponent, n, remains the same
4.31 x x 103 =
4.31 x x 104 =
4.70 x 104
1.8

40. Multiplication & Division w/ Scientific Notation
(4.0 x 10-5) x (7.0 x 103) =
(4.0 x 7.0) x (10-5+3) =
28 x 10-2 =
2.8 x 10-1
Multiply N1 and N2
Add exponents n1 and n2
Division
8.5 x 104 ÷ 5.0 x 109 =
(8.5 ÷ 5.0) x =
1.7 x 10-5
Divide N1 and N2
Subtract exponents n1 and n2
1.8

41. Practice Problems 1
. l l l l l cm
What is the length of the orange line?
1) cm
2) cm
3) cm

42. Practice Problems 2
State the number of significant figures in each of the following measurements.
A m
B L
C g
D m

43. Practice Problems 4
Classify each of the following as (1) exact or (2) measured
numbers.
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.

44. Practice Problems 5 A. Which answer(s) contain 3 significant figures?
1) ) ) x 103
B. All the zeros are significant in
1) ) ) x 103
C. The number of significant figures in 5.80 x 102 is
1) one 3) two 3) three

45. Practice Problems 6
In which set(s) do both numbers contain the same number of significant figures?
1) and 22.00
2) and 40
3) and

46. Significant Figures in
Calculations

47. Rounding Off Calculated Answers
In calculations,
answers must have the same number of significant figures as the measured numbers.
often, a calculator answer must be rounded off.
rounding rules are used to obtain the correct number of significant figures.
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48. Rounding Off Calculated Answers
When the first digit dropped is 4 or less,
the retained numbers remain the same.
rounded to 3 significant figures
drops the digits 32 = 45.8
When the first digit dropped is 5 or greater,
the last retained digit is increased by 1.
rounded to 2 significant figures
drops the digits 884 = 2.5 (increase by 0.1)

49. 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

50. Calculations with Measured Numbers
In calculations with
measured numbers,
significant figures or
decimal places are
counted to determine
the number of figures in
the final answer.
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51. Multiplication and Division
When multiplying or dividing use
the same number of significant figures as the measurement with the fewest significant figures.
rounding rules to obtain the correct number of significant figures.
Example:
x = = (rounded)
4 SF SF calculator SF

52. Addition and Subtraction
When adding or subtracting use
the same number of decimal places as the measurement with the fewest decimal places.
rounding rules to adjust the number of digits in the answer.
one decimal place
two decimal places
26.54 calculated answer
answer with one decimal place

53. Practice Problems 1 For each calculation, round the answer to give the
correct number of significant figures.
A =
1) ) )
B =
1) ) ) 40.7

54. Practice Problems 2 Adjust the following calculated answers to give
answers with three significant figures.
A cm
B g
C L

55. Practice Problems 3 Give an answer for the following with the correct
number of significant figures.
A x =
1) ) )
B ÷ =
1) ) ) 60
C x =
x 0.060
1) ) )

56. Solution 3
A x = 2) 9.2
B ÷ = 3) 60
C x = 2) 11 x
On a calculator, enter each number followed by the operation key.
2.54 x   =
= 11 (rounded)

57. Prefixes
&
Equalities

58. Prefixes
A prefix
in front of a unit increases or decreases the size of that unit.
prefix = value
1 kilometer = meters
1 kilogram = grams

59. Metric and SI Prefixes

60. Metric Equalities An equality
states the same measurement in two different units.
can be written using the relationships between two metric units.
Example: 1 meter is the same as 100 cm and 1000 mm.
1 m = cm
1 m = mm

61. Measuring Length Copyright © 2005 by Pearson Education, Inc.
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62. Measuring Volume Copyright © 2005 by Pearson Education, Inc.
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63. Measuring Mass
Several equalities can be written for mass in the metric (SI) system
1 kg = g
1 g = mg
1 mg = g
1 mg = µg
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64. Writing
Conversion Factors

65. Equalities Equalities
use two different units to describe the same measured amount.
are written for relationships between units of the metric system, U.S. units, or between metric and U.S. units.
For example,
1 m = mm
1 lb = oz
2.205 lb = 1 kg

66. Exact and Measured Numbers in Equalities
Equalities between units of
the same system are definitions and use exact numbers.
different systems (metric and U.S.) use measured numbers and count as significant figures.

67. Some Common Equalities

68. Conversion Factors A conversion factor
is a fraction obtained from an equality.
Equality: 1 in. = 2.54 cm
is written as a ratio with a numerator and denominator.
can be inverted to give two conversion factors for every equality.
1 in and cm
2.54 cm 1 in.

69. Conversion Factors in a Problem
A conversion factor
may be obtained from information in a word problem.
is written for that problem only.
Example 1:
The cost of one gallon (1 gal) of gas is $2.34.
1 gallon of gas and $2.34
$ gallon of gas

70. Percent as a Conversion Factor
A percent factor
gives the ratio of the parts to the whole.
% = Parts x 100
Whole
uses the same unit to express the percent.
uses the value 100 and a unit for the whole.
Example: A food contains 30% (by mass) fat.
30 g fat and 100 g food
100 g food 30 g fat

71. Percent Factor in a Problem
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
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72. Practice Problems 1 Write conversion factors for each pair of units.
A. liters and mL
B. hours and minutes
C. meters and kilometers

73. Practice Problems 2
Write the equality and conversion factors for each of the
following.
A. square meters and square centimeters
B. jewelry that contains 18% gold
C. One gallon of gas is $2.27

74. Problem Solving

75. Practice Problem 1
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?

76. Practice Problem 2
How many lb of sugar are in 120 g of candy if the candy is 25% (by mass) sugar?

77. Density Copyright © 2005 by Pearson Education, Inc.
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78. Density Density Compares the mass of an object to its volume.
Is the mass of a substance divided by its volume.
Density expression
Density = mass = g or g = g/cm3
volume mL cm3
Note: 1 mL = 1 cm3

79. Densities of Common Substances

80. Volume by Displacement
A solid completely submerged in water displaces its own volume of water.
The volume of the solid is calculated from the volume difference.
45.0 mL mL
= 9.5 mL = 9.5 cm3
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81. Density Using Volume Displacement
The density of the zinc object is
then calculated from its mass
and volume.
mass = g = 7.2 g/cm3 volume cm3
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82. Sink or Float
Ice floats in water because the density of ice is less than the density of water.
Aluminum sinks because its density is greater than the density of water.
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83. Density as a Conversion Factor
Density can be written as an equality.
For a substance with a density of 3.8 g/mL, the equality is
3.8 g = 1 mL
From this equality, two conversion factors can be written for density.
Conversion 3.8 g and mL
factors 1 mL g

84. Practice Problems 1
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?

85. Practice Problems 2
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?
33.0 mL
25.0 mL
object

86. Practice Problems 3
Which diagram correctly represents the liquid layers in the cylinder? Karo (K) syrup (1.4 g/mL), vegetable (V) oil (0.91 g/mL,) water (W) (1.0 g/mL) K W V V W K V W K

87. Practice Problems 4
The density of octane, a component of gasoline, is g/mL. What is the mass, in kg, of 875 mL of octane?

88. Practice Problems 5
If olive oil has a density of 0.92 g/mL, how many liters of olive oil are in 285 g of olive oil?

89. Practice Problems 6
A group of students collected 125 empty aluminum cans to take to the recycling center. If 21 cans make 1.0 lb aluminum, how many liters of aluminum (D=2.70 g/cm3) are obtained from the cans?

90. Practice Problems 7 1 2 3 25 g of aluminum 2.70 g/mL 45 g of gold
Which of the following samples of metals will displace the greatest volume of water?
25 g of aluminum
2.70 g/mL
45 g of gold
19.3 g/mL
75 g of lead
11.3 g/mL