Activity 151-1
Unit Conversions
Directions: This Guided Learning Activity (GLA) focuses on performing unit conversions. Part A
discusses how to write conversion factors and Part B uses conversion factors to perform single-step
conversions, and Part C discusses unit conversions for temperature and units with powers. The worksheet
is accompanied by instructional videos. See http://www.canyons.edu/Departments/CHEM/GLA/ for
additional materials.
Part A – Writing Conversion Factors
Converting between units is an important part of any science. Below is a table with measurements that are
common in chemistry. In the table, useful equalities are given.
Measure
Base unit
Abbreviation
Conversion to Know
Length
meter
m
1 in. = 2.54 cm
Mass
gram
g
1 lb = 453.6 g
Volume
liter
L
Temperature
⁰Celsius
⁰C
Energy
joule
1 L = 1.057 qt
3
1 mL = 1 cm
⁰C = (⁰F - 32)/1.8
K = ⁰C + 273.15
J
1 cal = 4.184 J
To convert between different systems of measure, conversion factors can be applied. A conversion factor
is written based on the equality between the two units. For example, a conversion factor for inches and
centimeters can be written two ways:
𝟐𝟐.𝟓𝟓𝟓𝟓 𝒄𝒄𝒎𝒎
𝟏𝟏 𝒊𝒊𝒊𝒊.
Or
𝟏𝟏 𝒊𝒊𝒊𝒊.
𝟐𝟐.𝟓𝟓𝟓𝟓 𝒄𝒄𝒄𝒄
Which of these two conversion factors is used depends on the desired conversion.
Example #1. Write two conversion factors for the following unit equalities:
a. 12 inches = 1 feet
b. 1 mile = 1.61 kilometer
𝟏𝟏𝟏𝟏 𝒊𝒊𝒊𝒊.
𝟏𝟏 𝒇𝒇𝒇𝒇
𝟏𝟏 𝒇𝒇𝒇𝒇
𝟏𝟏𝟏𝟏 𝒊𝒊𝒊𝒊.
c. 4 cups = 1 quart
Another set of conversion factors that you’ll need to know are the metric prefixes. The metric system
includes a set of prefixes that are based on factors of 10. These prefixes are extremely useful because they
are applied to many different types of measurements (e.g. length measurements, mass measurements, etc.)
Chemistry Guided Learning Activities
Activity 151 – 1
College of the Canyons
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The following table includes a shortened list of unit prefixes and equalities that Chemistry 151 students
should know.
Name
Prefix
Abbreviation
Equality (using meter as an example)
General Notation
Scientific Notation
nano-
n
1 m = 1,000,000,000 nm
1 m = 109 nm
micro-
μ
1 m = 1,000,000 μm
1 m = 106 μm
milli-
m
1 m = 1,000 mm
1 m = 103 mm
centi-
c
kilo-
k
1,000 m = 1 km
103 m = 1 km
mega-
M
1,000,000 m = 1 Mm
106 m = 1 Mm
giga-
G
1,000,000,000 m = 1 Gm
109 m = 1 Gm
1 m = 102 cm
1 m = 100 cm
(base units: g, m, L, J, M)
Example #2. Write two conversion factors that can be used to convert between:
𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝒎𝒎
a. meters and kilometers
𝟏𝟏 𝒌𝒌𝒌𝒌
b. microliters and liters
𝟏𝟏 𝒌𝒌𝒌𝒌
𝟏𝟏𝟏𝟏𝟏𝟏𝟏𝟏 𝒎𝒎
c. milligrams and kilograms
Often, conversion factors are not unit conversion factors per say, but are equivalencies that can be derived
from physical or chemical properties of substances or systems. For example, the density of a substance is
often used to relate its volume to its mass. Other common examples are given below.
Property
Common Units
density
velocity
concentration
percent composition
g/mL, g/cm3, lb/ft3
m/s, mi/hr
mol/L (e.g. M)
-
Example #3. Write a conversion factor for each of the following relationships.
a. Gold has a density of 19.32 g/cm3.
𝟏𝟏𝟏𝟏.𝟑𝟑𝟑𝟑 𝒈𝒈
𝟏𝟏 𝒄𝒄𝒎𝒎𝟑𝟑
b. 1 tablet contains 250 milligrams of acetaminophen.
𝟏𝟏 𝒄𝒄𝒎𝒎𝟑𝟑
𝟏𝟏𝟏𝟏.𝟑𝟑𝟑𝟑 𝒈𝒈
c. A water molecule has two hydrogen atoms.
d. Sodium chloride is 39.33% sodium.
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Part B – Performing Simple Conversions
To perform single step conversions, a conversion factor that relates the given value to the desired value is
identified. The given value is multiplied by the conversion factor so that the given units are divided from
the quantity.
𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅 𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖
� = 𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅𝒅 𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗
𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈 𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗𝒗 𝒙𝒙 �
𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈𝒈 𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖𝒖
When using this approach, it is important to include all units in calculations, treating them as algebraic
quantities.
Example #4. Perform the following conversions.
𝟐𝟐.𝟓𝟓𝟓𝟓 𝒄𝒄𝒄𝒄
�
𝟏𝟏 𝒊𝒊𝒊𝒊.
a. 𝟑𝟑𝟑𝟑. 𝟎𝟎 𝒊𝒊𝒊𝒊. �
b. 𝟓𝟓𝟓𝟓. 𝟎𝟎 𝒄𝒄𝒄𝒄
c. 𝟒𝟒. 𝟓𝟓𝟓𝟓 𝒙𝒙 𝟏𝟏𝟏𝟏𝟒𝟒 𝒏𝒏𝒏𝒏
= 𝟗𝟗𝟗𝟗. 𝟒𝟒 𝒄𝒄𝒄𝒄
=
=
𝒊𝒊𝒊𝒊.
𝒎𝒎
Sometimes the conversion factors are based on chemical or physical properties.
Example #5. Perform the following calculations.
a. The density of iron is 7.87 g/cm3. How much volume does 24.5 g of iron occupy?
𝟏𝟏 𝒄𝒄𝒎𝒎𝟑𝟑
𝟐𝟐𝟐𝟐. 𝟓𝟓 𝒈𝒈 �
� = 𝟑𝟑. 𝟏𝟏𝟏𝟏 𝒄𝒄𝒎𝒎𝟑𝟑
𝟕𝟕. 𝟖𝟖𝟖𝟖 𝒈𝒈
b. How far does light travel in 60.0 seconds? (c = 2.998 x 108 m/s)
𝟔𝟔𝟔𝟔. 𝟎𝟎 𝒔𝒔
=
𝒎𝒎
c. Magnesium chloride is 25.5% magnesium. How many grams of magnesium are present in 5.24
x104 g of magnesium chloride (MgCl2)?
𝟓𝟓. 𝟐𝟐𝟐𝟐 𝒙𝒙 𝟏𝟏𝟎𝟎𝟒𝟒 𝒈𝒈 𝑴𝑴𝑴𝑴𝑴𝑴𝒍𝒍𝟐𝟐
=
𝒈𝒈 𝑴𝑴𝑴𝑴
Part C – Special Cases in Unit Conversions – Temperature and Units with Powers
Temperature conversions between the Celsius scale and the Kelvin scale require only subtraction, since
the size of a degree in the Celsius and Kelvin scales is identical. When converting to and from the
Fahrenheit scale, both the size of the degree and the occurrence of 0° must be accounted for. The
conversion equations are given in the first table.
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Activity 151 – 1
College of the Canyons
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Example #6. Perform the following conversions:
a. 37.0 ℃ =
℉
b. 350 ℉ =
𝐾𝐾
c. What is absolute zero in the Fahrenheit scale?
Finally, to convert between units with powers, we must account for the power in the unit conversion. To
do so, the entire conversion equality is raised to the desired power. For example, the conversion factor
between cubic inches (in.3) and cubic centimeters (cm3) can be determined from the inches to centimeters
conversion factor.
We know: 𝟏𝟏 𝒊𝒊𝒊𝒊. = 𝟐𝟐. 𝟓𝟓𝟓𝟓 𝒄𝒄𝒄𝒄
Cubing the equality:
Example #7.
(𝟏𝟏 𝒊𝒊𝒊𝒊. = 𝟐𝟐. 𝟓𝟓𝟓𝟓 𝒄𝒄𝒄𝒄)𝟑𝟑
𝟏𝟏𝟑𝟑 𝒊𝒊𝒊𝒊.𝟑𝟑 = 𝟐𝟐. 𝟓𝟓𝟒𝟒𝟑𝟑 𝒄𝒄𝒎𝒎𝟑𝟑
𝟏𝟏 𝒊𝒊𝒊𝒊.𝟑𝟑 = 𝟏𝟏𝟏𝟏. 𝟒𝟒 𝒄𝒄𝒎𝒎𝟑𝟑
a. How many cubic centimeters (cm3) are equivalent to 2.00 in.3?
𝟏𝟏𝟏𝟏.𝟒𝟒 𝒄𝒄𝒎𝒎𝟑𝟑
�
𝟏𝟏 𝒊𝒊𝒊𝒊.𝟑𝟑
Using the calculated conversion factor from above: 𝟐𝟐. 𝟎𝟎𝟎𝟎 𝒊𝒊𝒊𝒊.𝟑𝟑 �
b. How many square meters does an 80. ft2 rug occupy? (1 ft = 12 in.)
= 𝟑𝟑𝟑𝟑. 𝟖𝟖 𝒄𝒄𝒎𝒎𝟑𝟑
Unit conversions are discussed further in GLA 151-2: Dimensional Analysis. Please refer to that
GLA for more guidance.
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Activity 151 – 1
College of the Canyons
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Part D – Extra Practice
1. Perform the following unit conversions.
a. 12 mg = ______________ lb.
b. 67.3 km = ______________ mm
c. 39.3 in. = ______________ cm
d. 60.0 cal = ______________ J
e. 1.2 x 10-9 mg = ______________ μg
f. 5.2 m3 = ______________ ft3
g. 62 °C = ______________ K
h. 12 L = ______________ cm3
i. 0.00245 m = ______________ in.
j. 1.00 g = ______________ oz. (1 lb. = 16 oz.)
k. 170 g/cm2 = ______________ lb/in2
l. 2.5 x 107 km = ______________ in.
m. 45 °F = ______________ °C
n. -264 °F = ______________ K
2. How many liters of air are in a room that is 1200 m3?
3. What is the volume of a 59.5 g silver spoon? (dAg = 10.5 g/cm3).
4. The combustion of one gallon of gasoline will produce approximately 8.39 kg of carbon dioxide (CO2).
What volume will the CO2 occupy? (dCO2 = 1.96 g/L).
5. The density of silver is 10.5 g/cm3. Express this density in terms of lb/ft3.
6. The USDA recommends that a person’s sodium intake be limited to 2,400 mg. Table salt is 39.33%
sodium. How many grams of table salt can Jenny consume without surpassing this limit? (Assume there
are no other sources of sodium in her diet.)
7. If one cup of coffee contains 95 milligrams of caffeine, how many cups of coffee will contain 5.00
grams of caffeine?
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Activity 151 – 1
College of the Canyons
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