Basic Mathematics for College Students

Use unit conversion factors to convert metric units of length.

Metric units of length are related as shown in the following table.

Metric Units of Length

1 kilometer (km) 1,000 meters 1 meter 10 decimeters (dm)

1 hectometer (hm) 100 meters 1 meter 100 centimeters (cm)

1 dekameter (dam) 10 meters 1 meter 1,000 millimeters (mm)

The abbreviation for each unit is written within parentheses.

We can use the information in the table to write unit conversion factors that can

be used to convert metric units of length. For example, in the table we see that

From this fact, we can write two unit conversion factors.

One advantage of the metric system is that multiplying or dividing by a unit

conversion factor involves multiplying or dividing by a power of 10.

To obtain the first unit conversion factor,

divide both sides of the equation 1 m 

100 cm by 100 cm. To obtain the second unit

conversion factor, divide both sides by 1 m.

100 cm

1 m

and  1

1 m

100 cm

 1

1 meter100 centimeters

3

458 Chapter 5 Ratio, Proportion, and Measurement

Self Check 3

Convert 860 centimeters to

meters.

Now TryProblem 31

Solution

On the ruler, the shorter tick marks divide each centimeter into 10 millimeters, as

shown. If we begin at the left end of the ruler and count by tens as we move right

to 3, and then add an additional 6 millimeters to that result, we find that the length

of the paper clip is 30 + 6 = 36 millimeters.

123456

10 mm 10 mm 10 mm 6 mm

Centimeters

EXAMPLE (^3) Convert 350 centimeters to meters.
StrategyWe will multiply 350 centimeters by a carefully chosen unit conversion
factor.
WHYIf we multiply by the proper unit conversion factor, we can eliminate the
unwanted units of centimeters and convert to meters.
Solution
To convert from centimeters to meters, we must choose a unit conversion factor
whose numerator contains the units we want to introduce (meters), and whose
denominator contains the units we want to eliminate (centimeters). Since there is
1 meter for every 100 centimeters, we will use
This is the unit we want to introduce.
 This is the unit we want to eliminate (the original unit).
1 m 
100 cm