14
Caution: It should be kept in mind that multiplying any expression by one does not change its value but
change its unit.
Writing a conversion factor as a ratio equal to 1
Using information from table1.3 and pick up a conversion factor such as
1 m = 10-3km
From this conversion factor, we can construct two ratios each equal to 1, namely,
1m
10 3 km
1 and
1
1m
10 3 km
In solving a problem, one should pick up the right ratio; the one that eliminate the unwanted unit and keep
the wanted.
Example 1.7
Convert 54 m to km.
Solution
The meter (m) is unwanted unit and the kilometer (km) is the wanted unit. Following the above steps of
conversion of units, one gets
10 3 km
(54 m) (
) 54 10 3 5.4 10 2 km
1m
Notice that we chose the second ratio with the meter (m) at the bottom because it cancels the meter (m)
unit from both quantities in the two parentheses. In some problems you are asked to continue this process
of multiplying by 1 as many times as necessary to complete the conversion (look at exercise 7 of
Chapter‟s 1 worksheet.)