Page 414 - Basic College Mathematics with Early Integers

S E C T I O N 5.4 I LENGTH: U.S. AND METRIC SYSTEMS OF MEASUREMENT 391

Concept Check Is this statement reasonable? “The screen of a home tele-
vision set has a 30-meter diagonal.”Why or why not?

Being comfortable with the metric units of length means gaining a “feeling” for
metric lengths, just as you have a “feeling” for the lengths of an inch, a foot, and a
mile.To help you accomplish this, study the following examples:
A millimeter is about the thickness of a 1 mm
large paper clip. 1 cm
A centimeter is about the width of a
large paper clip.
A meter is slightly longer than a yard.
A kilometer is about two-thirds of a mile. 1 mile
The width of this book is approximately 1 kilometer
21.5 centimeters.
The distance between New York City
and Philadelphia is about 160 kilometers.

2q centimeters is
about 1 inch.
2.54 cm
1.7 meters

7 millimeters
19 centimeters
1 inch
As with the U.S. system of measurement, unit fractions may be used to convert
from one unit of length to another. For example, let’s convert 1200 meters to kilo-
meters.To do so, we will multiply by 1 in the form of the unit fraction
1 km ; Units to convert to
1000 m ; Original units
Unit fraction
2
1200 m 1200 m 1 km 1200 km
1200 m = # 1 = # = = 1.2 km
1 1 1000 m 1000
The metric system does, however, have a distinct advantage over the U.S. sys-
tem of measurement: the ease of converting from one unit of length to another.
Since all units of length are powers of 10 of the meter, converting from one unit of
length to another is as simple as moving the decimal point. Listing units of length in
order from largest to smallest helps to keep track of how many places to move the
decimal point when converting.
Let’s again convert 1200 meters to kilometers.This time, to convert from meters
to kilometers, we move along the chart shown, 3 units to the left, from meters to
kilometers.This means that we move the decimal point 3 places to the left.
km hm dam m dm cm mm

3 units to the left
1200 m 1.200 km 1000 m 200 m

3 places to the left 1 km 0.2 km
Concept Check Answer
Thus, 1200 m = 1.2 km, as shown in the diagram. no; answers may vary