Basic Mathematics for College Students

460 Chapter 5 Ratio, Proportion, and Measurement

Self Check 5

Convert 5.15 centimeters to

kilometers.

Now TryProblem 39

Solution

To construct a conversion chart, we list the metric units of length from largest

(kilometers) to smallest (millimeters), working from left to right. Then we locate

the original units of meters and move to the conversion units of millimeters, as

shown below.

3 places to the right

We see that the decimal point in 2.4 should be moved 3 places to the right to

convert from meters to millimeters.

2.4 meters 2 400. millimeters 2,400 millimeters

Move 3 places to the right.

We can use the unit conversion factor method to confirm this result. Since

there are 1,000 millimeters per meter, we multiply 2.4 meters by the unit conversion

factor.

Write 2.4 m as a fraction: 2.4 m .

Multiply by a form 1:.

Multiply the fractions and simplify.



Multiply 2.4 by 1,000 by moving the decimal

 2,400 mm point 3 places to the right: 2 400.

 2.4#1,000 mm

Remove the common units of meters from

the numerator and denominator. Notice

that the units of millimeters remain.



2.4 m

1



1,000 mm

1 m

1,000 mm

1 m^

(^2) .4 m
2.4 m2.4 m^1
1
#1,000 mm
1 m
1,000 mm
1 m


km hm dam m dm cm mm
EXAMPLE (^5) Convert 3.2 centimeters to kilometers.
StrategyOn a conversion chart, we will count the places and note the direction
as we move from the original units of centimeters to the conversion units of
kilometers.
WHYThe decimal point in 3.2 must be moved the same number of places and in
that same direction to find the conversion to kilometers.
Solution
We locate the original units of centimeters on a conversion chart, and then move to
the conversion units of kilometers, as shown below.
5 places to the left
We see that the decimal point in 3.2 should be moved 5 places to the left to
convert centimeters to kilometers.
3.2 centimeters = 0.000032 kilometers = 0.000032 kilometers
Move 5 places to the left.
We can use the unit conversion factor method to confirm this result. To convert
to kilometers, we must use two unit conversion factors so that the units of
centimeters drop out and the units of kilometers remain. Since there is 1 meter for


km hm dam m dm cm mm