SI - Converting Units of Distance

Converting units of distance is fairly straightforward when all units are expressed within the metric system — provided that one has memorized the prefixes. The following example shows how to convert from kilometers to meters:

Q) How many meters is 8.5 kilometers?

Remembering that 1 kilometer = 1,000 meters:

A) 8.5 km. x 1,000 m./km. = 8,500 m.

But how was this done?

If 1 kilometer equals 1,000 meters, then it stands to reason that there are 1,000 meters per kilometer:

$$ 1 km. = 1,000 m.$$

In mathematics, the word "per" signifies division, allowing one to rewrite 1,000 meters per kilometer as a ratio:

$$ \frac{1,000 m.}{1 km.}$$

Multiplying the number of kilometers given with this ratio allows us to convert between kilometers and meters:

$$8.5 km. \times \frac{1,000 m.}{1 km.} = 8,500 m.$$


$$ \frac{8.5 km.}{1} \times \frac{1,000 m.}{1 km.} = 8,500 m.$$

Note how the units of kilometers (km.) in the two terms cancel each other out when multiplied with one another — leaving us with meters (m.).

$$ \frac{8.5 \cancel{km.}}{1} \times \frac{1,000 m.}{1 \cancel{km.}} = 8,500 m.$$

Getting into the habit of writing units down and canceling them out is one of quickest ways to check your work.

Even if you understand the concepts modeled by the equations you are using, the units must line up with one another to calculate the result.