Page 409 - Basic College Mathematics with Early Integers

Objectives 5.4 LENGTH: U.S. AND METRIC SYSTEMS OF MEASUREMENT

Define U.S. Units of Length and
Convert from One Unit to
Another. Objective Defining and Converting U.S. System
Units of Length
Use Mixed U.S. Units of Length.
In the United States, two systems of measurement are commonly used.They are the
Perform Arithmetic Operations United States (U.S.), or English, measurement system and the metric system. The
on U.S. Units of Length. U.S. measurement system is familiar to most Americans. Units such as feet, miles,
ounces, and gallons are used. However, the metric system is also commonly used in
Define Metric Units of Length
fields such as medicine, sports, international marketing, and certain physical sciences.
and Convert from One Unit to
We are accustomed to buying 2-liter bottles of soft drinks, watching televised cover-
Another.
age of the 100-meter dash at the Olympic Games, or taking a 200-milligram dose of
pain reliever.
Perform Arithmetic Operations
The U.S. system of measurement uses the inch, foot, yard, and mile to measure
on Metric Units of Length.
length. The following is a summary of equivalencies between units of length:
U.S. Units of Length

12 inches (in.) = 1 foot (ft)
3 feet = 1 yard (yd)
36 inches = 1 yard
5280 feet = 1 mile (mi)

To convert from one unit of length to another, we will use unit fractions. We
define a unit fraction to be a fraction that is equivalent to 1. Examples of unit frac-
tions are as follows:

Unit Fractions
12 in. 1 ft
= 1 or = 1 (since 12 in. = 1 ft)
1 ft 12 in.
3 ft 1 yd
= 1 or = 1 (since 3 ft = 1 yd)
1 yd 3 ft
5280 ft 1 mi
= 1 or = 1 (since 5280 ft = 1 mi)
1 mi 5280 ft

Remember that multiplying a number by 1 does not change the value of the
number.

PRACTICE 1 Example 1 Convert 8 feet to inches.
Convert 6 feet to inches.
Solution: We multiply 8 feet by a unit fraction that uses the equality
units to convert to
12 inches = 1 foot. The unit fraction should be in the form or,
original units
12 inches
in this case, . We do this so that like units will divide out to 1, as shown.
1 foot
8 ft
8 ft = # 1
1
8 ft 12 in. 12 in. Copyright 2012 Pearson Education, Inc.
= # Multiply by 1 in the form of .
1 1 ft 1 ft
#
Answer = 8 12 in.
1. 72 in. = 96 in. Multiply.
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