1. Chapter 2 Measurements
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2. 2.1 Units of Measurement
Learning Goal Write the names and abbreviations for the metric or SI units used in measurements of length, volume, mass, temperature, and time

3. Chapter 2 Readiness Key Math Skills Identifying Place Values (1.4A)
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4. The International System of Units (SI)
Chemists use the metric system and the International System of Units (SI) for measurement when they
measure quantities
do experiments
solve problems

5. Units of Measurement and Their Abbreviations

6. Metric System
Prefixes convert the base units into units that are appropriate for the item being measured.
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7. Length
Length is measured in
units of meters (m) in both the metric and SI systems
units of centimeters (cm) by chemists

8. Length
Useful relationships between units of length include:
1 m = yd
1 m = in.
1 m = 100 cm
2.54 cm = 1 in.

9. Volume
The most commonly used metric units for volume are the liter (L) and the milliliter (mL).
A liter is a cube 1 decimeter (dm) long on each side.
A milliliter is a cube 1 centimeter (cm) long on each side.
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10. Volume
Volume, the space occupied by a substance,
is measured using units of m3 in the SI system
is commonly measured in liters (L) and milliliters (mL) by chemists

11. Volume
Useful relationships between units of volume include:
1 m3 = 1000 L
1 L = 1000 mL
1 mL = 1 cm3
1 L = qt
946.3 mL = 1 qt

12. Mass
The mass of an object, a measure of the quantity of material it contains,
is measured on an electronic balance
has the SI unit of kilogram (kg)
is often measured by chemists in grams (g)

13. Mass
Useful relationships between units of mass include:
1 kg = 1000 g
1 kg = lb
453.6 g = 1 lb

14. Temperature
By definition temperature is a measure of the average kinetic energy of the particles in a sample.
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15. Temperature
In scientific measurements, the Celsius and Kelvin scales are most often used.
The Celsius scale is based on the properties of water.
0 C is the freezing point of water.
100 C is the boiling point of water.
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16. Temperature The kelvin is the SI unit of temperature.
It is based on the properties of gases.
There are no negative Kelvin temperatures.
K = C
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17. Temperature
The Fahrenheit scale is not used in scientific measurements.
F = 9/5(C) + 32
C = 5/9(F − 32)
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18. Time
Time is based on an atomic clock and is measured in units of seconds (s) in both the metric and SI systems.

19. Learning Check
For each of the following, indicate whether the unit describes
(1) length, (2) mass, or (3) volume
A. A bag of onions has a mass of 2.6 kg.
B. A person is 2.0 m tall.
C. A medication contains 0.50 g of aspirin.
D. A bottle contains 1.5 L of water.

20. Solution
For each of the following, indicate whether the unit describes
(1) length, (2) mass, or (3) volume
A. A bag of onions has a mass of 2.6 kg (2)
B. A person is 2.0 m tall (1)
C. A medication contains 0.50 g of aspirin (2)
D. A bottle contains 1.5 L of water (3)

21. 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 mass of a lemon is _____.
(1) 12 oz (2) kg (3) 0.6 lb
C. The temperature is _____.
(1) 85 ºC (2) 255 K (3) 45 ºF

22. Solution
Identify the measurement that has an SI unit.
A. John’s height is______. (3) 2.1 m
B. The mass of a lemon is _____. (2) kg
C. The temperature is _____. (2) 255 K

23. Density
Learning Goal Calculate the density of a substance; use the density to calculate the mass or volume of a substance.

24. d = m V Derived Units Density is a physical property of a substance.
It has units (g/mL, for example) that are derived from the units for mass and volume.
d = m V
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25. Density Substances that have
higher densities contain particles that are closely packed together
lower densities contain particles that are farther apart
Metals such as gold and lead have higher densities because their atoms are packed closely together.
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26. Density, Units
In the metric system, densities of solids, liquids, and gases are expressed with different units.
The density of a solid or liquid is usually given in
grams per cubic centimeter (g/cm3)
grams per milliliter (g/mL)
The density of a gas is usually given in grams per liter (g/L).
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27. Density of Common Substances
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28. Guide to Calculating Density
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29. Learning Check
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?
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30. Solution
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?
Step 1 Given g; cm3
Need density, in g/cm3
Step 2 Plan Write the density expression.
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31. Solution
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? Step 3 Express mass in grams and volume in cm3.
mass = 50.0 g volume = 22.2 cm3
Step 4 Set up problem, calculate.
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32. Link to the Environment
The oil pumped out of the ground is called crude oil, or petroleum. It is mostly made of hydrocarbons, or compounds that contain only carbon and hydrogen.
In April 2010, an oil rig in the Gulf of Mexico exploded, causing the largest oil spill in U.S. history.
It leaked a maximum of 10 million liters a day into the Gulf of Mexico.
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33. Link to the Environment
Because the density of this oil, 0.8 g/mL, was less than that of water, which is 1.00 g/mL, it floated on the surface, spreading a thin layer of oil over a very large surface.
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34. Density of Solids
The density of a solid is calculated from its mass and volume.
When a solid is submerged, it displaces a volume of water equal to the volume of the solid.
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35. Density of Solids
In the figure below, the water level rises from 35.5 mL to 45.0 mL after the zinc object is added.
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36. Learning Check
Scuba divers use lead weights to counteract their buoyancy in water. What is the density of a lead weight that has a mass of 226 g and displaces 20.0 cm3 of water when submerged?
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37. Solution
What is the density of a lead weight that has a mass of 226 g and displaces 20.0 cm3 of water when submerged?
Step 1 Given 226 g lead
20.0 cm3 water displaced
Need density (g/cm3) of lead
Step 2 Plan. Write the density expression.
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38. Solution
What is the density of a lead weight that has a mass of 226 g and displaces 20.0 cm3 of water when submerged?
Step 3 Express mass in grams and volume
in cm3.
mass of lead weight = 226 g
volume of water displaced = 20.0 cm3
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39. Solution
What is the density of a lead weight that has a mass of 226 g and displaces 20.0 cm3 of water when submerged?
Step 4 Set up problem, calculate.
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40. Density as a Conversion Factor
Density can be used as a conversion factor between a substance’s mass and volume.
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41. Learning Check
If the density of milk is 1.04 g/mL, how many grams of milk are in 0.50 qt?
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42. Solution
If the density of milk is 1.04 g/mL, how many grams of milk are in 0.50 qt?
Step 1 Given qt milk
density of milk is 1.04 g/mL
Need grams of milk
Step 2 Write a plan.
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43. Solution
If the density of milk is 1.04 g/mL, how many grams of milk are in 0.50 qt?
Step 3 Write equalities, conversion factors.
1 L = qt L = 1000 mL
1.04 g = 1 mL
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44. Solution
If the density of milk is 1.04 g/mL, how many grams of milk are in 0.50 qt?
Step 4 Set up problem, calculate.
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45. Concept Map
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46. Learning Goal Write a number in scientific notation.

47. Scientific Notation
Scientific notation is used to write very large or very small numbers such as
the width of a human hair, m, which is also written as 8 × 10−6 m
the number of hairs on a human scalp, , which is also written as 1 × 105 hairs
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48. Writing Numbers in Scientific Notation
A number written in scientific notation contains a coefficient and a power of ten.
coefficient power unit
of ten
× m
The coefficient is at least 1 but less than 10.
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49. Scientific Notation In science, we deal with some very LARGE numbers:
1 mole =
In science, we deal with some very SMALL numbers:
Mass of an electron = kg

50. Imagine the difficulty of calculating the mass of 1 mole of electrons!kg x
???????????????????????????????????

51. . 9 8 7 6 5 4 3 2 1
Step #1: Insert an understood decimal point
Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form 2.5 x 10n

52. 2.5 x 109
The exponent is the number of places we moved the decimal.

53. 0.0000579 1 2 3 4 5 Step #2: Decide where the decimal must end
up so that one number is to its left
Step #3: Count how many places you bounce
the decimal point
Step #4: Re-write in the form 5.79 x 10n

54. 5.79 x 10-5
The exponent is negative because the number we started with was less than 1.

55. Writing Numbers in Scientific Notation
The number of spaces moved to obtain a coefficient between 1 and 10 is shown as a power of ten.
= × 104
move decimal 4 spaces left
= × 10−3
move decimal 3 spaces right
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56. Some Powers of Ten
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57. Some Measurements in Scientific Notation
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58. Comparing Numbers in Standard and Scientific Notation
Standard Format Scientific Notation Diameter of the Earth
m × 107 m
Mass of a human
68 kg × 101 kg
Diameter of a virus
cm 3 × 10−7 cm
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59. Scientific Notation and Calculators
You can enter a number written in scientific notation on many calculators using the EE or EXP key.
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60. Scientific Notation and Calculators
When a calculator display appears in scientific notation, it is shown as a number between 1 and 10, followed by a space and the power (exponent).
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61. Scientific Notation and Calculators
On many scientific calculators, a number is converted to scientific notation, using the appropriate keys.
nd or 3rd function key SCI
Key Key
= 5.2 −04 or 5.2−04 = 5.2 × 10−4
Calculator display
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62. Guide to Writing a Number in Scientific Notation
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63. Learning Check
Write the following number in the correct scientific notation, g.
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64. Move the decimal 5 places to the right, to give a coefficient of 5.8.
Solution
Write the following number in the correct scientific notation, g.
Step 1 Move the decimal point to obtain a coefficient that is at least 1 but less than
Move the decimal 5 places to the right, to give a coefficient of 5.8.
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65. Step 2 Express the number of places moved as a power of 10.
Solution
Write the following number in the correct scientific notation, g.
Step 2 Express the number of places moved as a power of 10.
Moving the decimal 5 places to the right gives a power of −5.
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66. Solution
Write the following number in the correct scientific notation, g.
Step 3 Write the product of the coefficient multiplied by the power of 10 with the unit. 5.8 × 10−5 g
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67. Select the correct scientific notation for each. A. 0.000 008
Learning Check
Select the correct scientific notation for each. A
(1) 8 × 106 (2) 8 × 10−6 (3) 0.8 × 10−5 B
(1) 7.2 × 104 (2) 72 × 103 (3) 7.2 × 10−4
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68. Select the correct scientific notation for each. A. 0.000 008
Solution
Select the correct scientific notation for each. A
(Move the decimal 6 places to right.)
(2) 8 × 10−6 B
(Move the decimal 4 places to the left.)
(1) 7.2 × 104
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69. Write each as a standard number. A. 2.0 × 10−2
Learning Check
Write each as a standard number.
A. 2.0 × 10−2
(1) 200 (2) (3) 0.020
B. 1.8 × 105
(1) (2) (3)
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70. Write each as a standard number. A. 2.0 × 10−2 (3) 0.020 B. 1.8 × 105
Solution
Write each as a standard number.
A. 2.0 × 10−2
(3) 0.020
B. 1.8 × 105
(1)
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71. Dimensional Analysis
We use dimensional analysis to convert one quantity to another.
Most commonly, dimensional analysis utilizes conversion factors (e.g., 1 in. = 2.54 cm)
1 in.
2.54 cm or
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72. Dimensional Analysis
Use the form of the conversion factor that puts the sought-for unit in the numerator:
Given unit 
 desired unit
desired unit
given unit
Conversion factor
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73. Dimensional Analysis For example, to convert 8.00 m to inches,
convert m to cm
convert cm to in.
8.00 m 
100 cm
1 m
1 in.
2.54 cm 
315 in. 
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74. Uncertainty in Data
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75. Uncertainty in Measurements
Different measuring devices have different uses and different degrees of accuracy.
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76. Accuracy versus Precision
Accuracy refers to the proximity of a measurement to the true value of a quantity.
Precision refers to the proximity of several measurements to each other.
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77. Accuracy and Precision

78. Accuracy and Precision
Low accuracy, high precision
High accuracy, low precision
High accuracy, high precision

79. Accuracy and Precision Accepted mass of the object is 10.91 g
Trails
Mass (g) 1
11.50 2
11.20 3
10.50 4
10.60 5
10.30
Poor precision, but good accuracy

80. Accuracy and Precision mass of object has actual mass of 25.11 g
Data Set 1
Data Set 2
Data Set 3
Data Set 4
24.06 g
25.12 g
23.76 g
26.51 g
28.09
25.09 g
23.80 g
25.08 g
29.56 g
25.14 g
23.78 g
23.63 g
Data set 1 neither accurate or precise
Data set 2 accurate and precise
Data set 3 precise, not accurate
Data set 4 accurate (based on average), but not precise

81. Significant Figures
The term significant figures refers to digits that were measured.
When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.
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82. Significant Figures A number is a significant figure if it is
Not a zero
One or more zeros between nonzero digits
One or more zeros at the end of a decimal number
In the coefficient of a number written in scientific notation
2. A zero is not significant if it is
At the beginning of a decimal number written in scientific notation
Used as a placeholder in a large number without a decimal point
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83. Rules for Counting Significant Figures
55.32 has
4 significant figures

84. has
5 significant figures

85. has
1 significant figures

86. has
6 significant figures

87. Sig Fig In Class Practice
How many significant figures in each of the following? 
1 sig figs 
2 sig figs
3 sig figs
501  
4 sig figs 
1 sig figs 
4 sig figs

88. Sig Fig In Class Practice
How many significant figures in each of the following? 
6 sig figs 
1 sig figs
4 sig figs  
5 sig figs 
3 sig figs 
2 sig figs

89. Sig Fig In Class Practice
How many significant figures in each of the following? 
4 sig figs 
4 sig figs
3 sig figs  
5 sig figs 
4 sig figs
154 
3 sig figs

90. Sig Fig In Class Practice
How many significant figures in each of the following? 
3 sig figs 
5 sig figs

91. Significant Figures
When addition or subtraction is performed, answers are rounded to the least significant decimal place.
When multiplication or division is performed, answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation.
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92. calculated answers are usually rounded off
Rounding Off
In calculations
calculated answers are usually rounded off
rounding rules are used to obtain the correct number of significant figures
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93. Rules for Rounding Off
1. If the first digit to be dropped is 4 or less, then it and all following digits are simply dropped from the number.
2. If the first digit to be dropped is 5 or greater, then the last retained digit is increased by 1.
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94. Rounding Off and Significant Figures
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95. Learning Check
Adjust the following calculated answers to give answers with three significant figures:
A cm
B g
8.2 L
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96. Solution
Adjust the following calculated answers to give answers with three significant figures:
A cm 825 cm
B g g
8.2 L L
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97. Multiplication and Division with Measured Numbers
In multiplication and division, the final answer is written to have the same number of significant figures (SFs) as the measurement with the fewest SFs.
For example,
24.65 × =  17
4 SF SF Calculator Final answer
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98. = 4  4.00 Adding Significant Zeros
When the calculator answer is a small whole number and more significant figures are needed, we can add one or more zeros.
For example,
= 
3 SF Calculator Final answer
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99. Addition and Subtraction with Measured Numbers
In addition or subtraction, the final answer is written so that it has the same number of decimal places as the measurement having the fewest decimal places.
For example,
Thousandths place
Tenths place
Calculator display
Answer, rounded off to tenths place
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100. Learning Check
Give an answer for each with the correct number of significant figures.
2.19 × 4.2 =
(1) 9 (2) 9.2 (3) 9.198
B × =
× 0.060
(1) 11.3 (2) (3)
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101. Solution
Give an answer for each with the correct number of significant figures.
A × = (2) 9.2
B × = (2) 11
× 0.060
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102. Learning Check
For each calculation, round the answer to give the correct number of digits.
A =
(1) 257 (2) (3)
B – =
(1) (2) (3) 40.7
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103. Solution A. 235.05 Hundredths place +19.6 Tenths place + 2 Ones place
rounds to answer (1)
B Thousandths place
– Tenths place
rounds to answer (3)
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