Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
6.5 Metric – U.S. Customary Measurement Conversions
Since most of the world uses the metric system of measurement, we often need to know how to convert back
and forth between U.S. Customary measurements and metric measurements. The good news is that we can use
unit fractions using the relationships in the tables below! (It is also useful to have some of these relationships
memorized so you can make sense of the units just in case you find yourself traveling outside of the U.S.)
U.S. Customary to Metric
Metric to U.S. Customary
Length
1 in. = 2.54 cm
1 ft  0.30 m
1 yd  0.91 m
1 mi  1.61 km
Length
1 cm  0.39 in.
1 m  3.28 ft
1 m  1.09 yd
1 km  0.62 mi
Mass (Weight)
1 oz  28.35 g
1 lb  0.45 kg
Mass (Weight)
1 g  0.035 oz
1 kg  2.20 lbs
Volume (Capacity)
1 fl oz  0.03 L
1 pt  0.47 L
1 qt  0.95 L
1 gal  3.79 L
Volume (Capacity)
1 L  33.80 fl oz
1 L  2.10 pt
1 L  1.06 qt
1 L  0.26 gal
Example 1: Use unit fractions to convert 8.3 meters to yards.
Round your answer to the nearest tenth if necessary.
Solution:
8.3 m
1
Write down what is given over denominator 1.
There is a direct relationship between meters and yards: 1 m  1.09 yd
1m
1.09 yd
We have two choices for the unit fraction,
.
or
1.09 yd
1m
Choose
8.3 m  1.09 yd 


1  1m 

8.3  1.09 yd 


1  1 
1.09 yd
since the denominator has the unit we want to cancel.
1m
Write the unit fraction to the right of what is given and divide out units.
Notice we are left with the units that the problem is asking for.
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions

8.3 1.09 yd
1 1
Multiply the numerators. Multiply the denominators.

9.047
yd
1
Divide the numerator by the denominator.
 9.047 yd
Round to the nearest tenth.
 9.05 yd
So 8.3 m  9.05 yd .
Note: We could have also used the relationship from the U.S. Customary to Metric table: 1 yd  0.91 m
8.3 m  1 yd 


1  0.91 m 
8.3 1 yd
1 0.91
8.3

yd
0.91

 9.120879121 yd
Round to the nearest tenth.
 9.12 yd
Notice that the answer is slightly different from the 9.05 yd above!
This is because the values in both of the tables are rounded.
So which relationship is better? 1 m  1.09 yd or 1 yd  0.91 m?
In this course both relationships are fine to use, however, you may want to consider a few things:
1) Your instructor (or perhaps boss) will often indicate which one they prefer you to use. Make sure
you follow their instructions.
2) Some students prefer using 1 m  1.09 yd since they don’t have to divide. (This is helpful if you
ever find yourself without a calculator where it may be more difficult to divide decimal numbers
than to multiply them.)
3) Sometimes only one of the relationships is given so you don’t have to worry about choosing the one
that gives you the quickest computation.
You Try It 1: Use unit fractions to perform the following conversions.
Round your answers to the nearest tenth if necessary.
a) 23 m to yds
b) 40 cm to in.
c) 5 mi to km
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Example 2: Use unit fractions to convert 136 pounds to kilograms.
Round your answer to the nearest tenth if necessary.
Solution:
136 lbs
1
Write down what is given over denominator 1.
There is a direct relationship between lbs and kg: 1 kg  2.2 lbs
We have two choices for the unit fraction,
Choose
136 lbs  1 kg 


1
 2.2 lbs 
1 kg
2.2 lbs
or
.
2.2 lbs
1 kg
1 kg
since the denominator has the unit we want to cancel.
2.2 lbs
Write the unit fraction to the right of what is given and divide out units.

136  1 kg 


1  2.2 
Notice we are left with the units that the problem is asking for.

136 1 kg
1 2.2
Multiply the numerators. Multiply the denominators.

136
kg
2.2
Divide the numerator by the denominator.
 61.81 kg
Round to the nearest tenth.
 61.8 kg
So 136 lbs  61.8 kg .
Note: We could have also used the relationship from the U.S. Customary to Metric table: 1 lb  0.45 kg
We would have obtained 136 lbs  61.2 kg , a slightly different answer.
You Try It 2: Use unit fractions to perform the following conversions.
Round your answers to the nearest tenth if necessary.
a) 240 lbs to kg
b) 3.5 kg to lbs
c) 8 oz to g
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Example 3: Use unit fractions to convert 18.2 gal to liters.
Round your answer to the nearest tenth if necessary.
Solution:
18.2 gal
1
Write down what is given over denominator 1.
There is a direct relationship between gallons and liters: 1 gal  3.79 L
We have two choices for the unit fraction,
Choose
18.2 gal  3.79 L 


 1 gal 
1


1 gal
3.79 L
.
or
3.79 L
1 gal
3.79 L
since the denominator has the unit we want to cancel.
1 gal
Write the unit fraction to the right of what is given and divide out units.

18.2  3.79 L 


1  1 
Notice we are left with the units that the problem is asking for.

18.2  3.79 L
1 1
Multiply the numerators. Multiply the denominators.

68.978
L
1
Divide the numerator by the denominator.
 68.978 L
Round to the nearest tenth.
 69.0 L
So 18.2 gal  69.0 L .
Note: We could have also used the relationship from the U.S. Customary to Metric table: 1 L  0.26 gal
We would have obtained 18.2 gal = 70 L, a slightly different answer.
You Try It 3: Use unit fractions to perform the following conversions.
Round your answers to the nearest tenth if necessary.
a) 3.5 gal to L
b) 5 L to qts
c) 9.8 pts to L
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Example 4: Use unit fractions to convert 4.7 kilograms to ounces.
Round your answer to the nearest tenth if necessary.
Solution:
Write down what is given over denominator 1.
4.7 kg
1
There is no direct relationship between kilograms and ounces!
Write down any relationships from the tables involving kilograms and ounces:
1 g  0.035 oz
1 kg  2.20 lbs
1 oz  28.35 g
1 lb  0.45 kg
Figure out a path to get from kilograms to ounces: kilograms  grams  ounces
Notice that we can use what we know from Section 6.4 to convert kilograms to grams!
We use the direct relationship 1 kg = 1000 grams to set up a unit fraction to take care of the
conversion all at one time.
Choose the appropriate unit fractions and write them in order to the right of what is given.
1000 g
since we want to cancel out kilograms and be left with grams.
1 kg
1 oz
Then choose
since we want to cancel out grams and be left with ounces.
28.35 g
First choose
4.7 kg  1000 g   1 oz 



1  1 kg   28.35 g 
Now divide out units to make sure you will be left with ounces in the final answer.
4.7 kg  1000 g

1  1 kg

  1 oz

  28.35 g





4.7  1000  1 oz 



1  1  28.35 
Multiply the numerators. Multiply the denominators.

4.7 1000 1 oz
1 1  28.35
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions

4700
oz
28.35
Divide the numerator by the denominator.
 165.7848325 oz
Round to the nearest tenth.
 165.8 oz
Note: We could have also taken a slightly different path to get to ounces: kilograms  pounds  ounces
1 kg  2.2 lbs
and
1 lb = 16 oz (from the U.S. Customary relationships inSection 6.3)
4.7 kg  2.2 lbs   16 oz 



1  1 kg   1 lb 
4.7  2.2 16 oz
1 1 1
165.44

oz
1

 165.44 oz
Round to the nearest tenth.
 165.4 oz (a slightly different answer from 165.8 oz above)
Does it really matter which path we take?
In this course it really should not be an issue as long as you are showing the correct unit fraction set-up to
convert from the given units to the units the problem is asking for. We always recommend asking your
instructor or a tutor to check your work for a few of these types of homework problems so they can provide the
proper feedback to you.
You Try It 4: Use unit fractions to convert 5.3 kilograms to ounces.
Round your answer to the nearest tenth if necessary.
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Once we are comfortable with choosing the appropriate unit fractions to convert back and forth between U.S.
Customary and metric units, we can combine what we have learned from Sections 6.3, 6.4, and this section to
answer the following types of problems.
Example 5: The price of milk is $3.37 per gallon. Find the price per liter.
Solution:
Rewrite each “per” statement:
$3.37 per gallon =
$3.37
1 gal
Now we can see that the problem wants us to convert
price per liter =
price ($)
L
$3.37
price ($)
to
.
1 gal
L
Notice that there are two types of units involved: money and capacity
Both monies are already in dollars so we only need to perform one conversion: gallons  liters
Choose the appropriate unit fraction and attach it to the right of what is given.
Attach
1 gal
to convert gallons to liters.
3.79 L
$3.37  1 gal 


1 gal  3.79 L 
Now divide out units to make sure you will be left with
price ($)
in the final answer.
L
$3.37  1 gal 


1 gal  3.79 L 

$3.37  1 


1  3.79 L 
Multiply the numerators. Multiply the denominators.

$3.37 1
1  3.79 L

$3.37
3.79 L
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Divide the numerator by the denominator.

Round to the nearest cent.
$0.889182058
L
 $0.89 per liter
You Try It 5: The price of gas is $4.28 per gallon. Find the price per liter.
Example 6: The speed limit on a highway in Montreal is 120 kilometers per hour. How fast is this in miles
per hour? Round your answer to the nearest tenth if necessary.
Solution:
Rewrite each “per” statement:
120 kilometers per hour =
120 km
1 hr
Now we can see that the problem wants us to convert
miles per hour =
mi
hr
120 km
mi
to
.
1 hr
hr
Notice that there are two types of units involved: length and time
Both times are already in hours so we only need to perform one conversion: kilometers  miles
Choose the appropriate unit fraction and attach it to the right of what is given.
Attach
1 mi
to convert kilometers to miles.
1.61 km
120 km  1 mi 


1 hr  1.61 km 
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Now divide out units to make sure you will be left with
120 km
1 hr

mi
in the final answer.
hr
 1 mi 


 1.61 km 
120  1 mi 


1 hr  1.61 
Multiply the numerators. Multiply the denominators.

120 1 mi
1 1.61 hr

120 mi
1.61 km
Divide the numerator by the denominator.

Round to the nearest tenth.
74.53416149 mi
hr
 74.5 miles per hour
You Try It 6: The speed limit on a road in Montreal is 75 kilometers per hour. How fast is this in miles
per hour? Round your answer to the nearest tenth if necessary.
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Temperature
When you travel outside of the United States. length, mass, and volume are not the only measurements that
differ. In the U.S., temperature is measured in degrees Fahrenheit ( F ). Scientists and the rest of the world use
degrees Celsius ( C ) to measure temperature. Because of this, temperature measured in Celsius is categorized
as belonging to the metric system, while temperature measured in Fahrenheit is categorized as belonging to the
U.S. Customary system.
Two of the most important benchmarks that help us understand the degrees Celsius in relation to degrees
Fahrenheit are the freezing and boiling points of water.
Freezing and Boiling Points of Water
Water freezes at 0 degrees Celsius ( 0 C ). This is 32 degrees Fahrenheit ( 32 F ).
Water boils at 100 degrees Celsius ( 100 C ). This is 212 degrees Fahrenheit ( 212 F ).
Here are some typical measurements in both Celsius and Fahrenheit:
Celsius
Fahrenheit
water boils
100 C
212 F
hot coffee
60 C
140 F
hot bath water
50 C
122 F
normal body temperature
37 C
98.6 F
summer day
30 C
86 F
room temperature
20 C
68 F
winter day in California
10 C
50 F
water freezes
0C
32 F
super cold winter day
18 C
0F
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Example 7: Circle the most reasonable metric temperature for each situation.
a) Warm summer day:
29 C
5 C
b) Iced tea:
5C
64 C
90 C
30 C
Solution:
a) 29 C because the other temperatures are both above the temperature of hot coffee. Way too
hot!
b) 5 C because 5 C is below freezing which means that the tea would be frozen solid and
30 C is the temperature of a warm summer day which means that the tea would no longer be
“iced” tea.
You Try It 7: Circle the most reasonable metric temperature for each situation.
a) Inside a freezer:
 10 C
5C
b) Set the living room thermostat at:
c) Wear a jacket outside because it is:
25 C
8C
12 C
21 C
28 C
71 C
50 C
Now that we have a better understanding of Celsius-Fahrenheit relationships we can look at using formulas to
convert back and forth between Celsius and Fahrenheit.
Celsius and Fahrenheit Conversion Formulas
Converting from F to C
C
5
 F  32 
9
Converting from C to F
9
F  C  32
5
Remember, once you plug in the given temperature to the formula, use the order of operations to simplify.
Use your calculator to help with any computations that involve fractions or decimals.
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Example 8: Convert 20 F to Celsius. Round your answer to the nearest degree if necessary.
Solution:
Since we want to find Celsius, write the formula that already has C isolated on one side.
C
5
 F  32 
9
Substitute F  20 into the formula.
C
5
 20  32 
9
Use the order of operations to simplify.
Perform the subtraction inside the parentheses first.
C
5
 12 
9
Now multiply.
C
20
3
C  6.6
Round to the nearest degree.
C  7
You Try It 8: Convert 59 F to Celsius. Round your answer to the nearest degree if necessary.
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2015 Campeau
Math 40
Prealgebra
Section 6.5 – Metric – U.S. Customary Measurement Conversions
Example 9: Convert 25 C to Fahrenheit. Round your answer to the nearest degree if necessary.
Solution:
Since we want to find Fahrenheit, write the formula that already has F isolated on one side.
9
F  C  32
5
Substitute C  25 into the formula.
F
9
 25  32
5
Use the order of operations to simplify.
Perform the multiplication first.
F  45  32
Now add.
F  77
You Try It 9: Convert 32 C to Fahrenheit. Round your answer to the nearest degree if necessary.
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