Measurement Examples And Worksheet - A-64 Appendix 5 Page 3
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36A-65
V.1 American Units of Measurement
Convert from one American unit of length to another.
3
To convert from one unit of length to another, we use unit conversion factors. To find
the unit conversion factor between yards and feet, we begin with this fact:
3 ft
1 yd
If we divide both sides of this equation by 1 yard, we get
1 yd
3 ft
1 yd
1 yd
3 ft
1 yd
1
Simplify the right side of the equation. A number divided by itself is 1:
1
.
1 yd
1 yd
3 ft
The fraction
is called a unit conversion factor, because its value is 1. It can be
1 yd
read as “3 feet per yard.” Since this fraction is equal to 1, multiplying a length by this
fraction does not change its measure; it changes only the units of measure.
To convert units of length in the American system of measurement, we use the
following unit conversion factors. Each conversion factor shown below is a form of 1.
Use the unit
Use the unit
To convert from
conversion factor
To convert from
conversion factor
12 in.
1 ft
feet to inches
inches to feet
1 ft
12 in.
1 yd
3 ft
yards to feet
feet to yards
1 yd
3 ft
1 yd
36 in.
yards to inches
inches to yards
1 yd
36 in.
5,280 ft
1 mi
miles to feet
feet to miles
1 mi
5,280 ft
Self Check 3
3
EXAMPLE
Convert 8 yards to feet.
Convert 9 yards to feet.
Strategy
We will multiply 8 yards by a carefully chosen unit conversion factor.
Now Try
Problem 35
WHY
If we multiply by the proper unit conversion factor, we can eliminate the
unwanted units of yards and convert to feet.
Solution
To convert from yards to feet, we must use a unit conversion factor that relates
feet to yards. Since there are 3 feet per yard, we multiply 8 yards by the unit
3 ft
conversion factor
.
1 yd
8 yd
8 yd
3 ft
Write 8 yd as a fraction:
8 yd
.
1
8 yd
3 ft
Then multiply by a form of 1:
.
1
1 yd
1 yd
8 yd
3 ft
Remove the common units of yards from the numerator
and denominator. Notice that the units of feet remain.
1
1 yd
8 3 ft
Simplify.
24 ft
Multiply: 8 3
24.
8 yards is equal to 24 feet.
Success Tip
Notice that in Example 3, we eliminated the units of yards and
introduced the units of feet by multiplying by the appropriate unit conversion
factor. In general, a unit conversion factor is a fraction with the following form:
Unit we want to introduce
Numerator
Unit we want to eliminate
Denominator
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