Another equivalent way of
changing units is to
multiply by a fraction that is referred to a conversion factor.
The expression for the
fraction can be
written if you know the relationship between the units in
words.
Example statement in words:
There are 1000 mm per metre.
Per means divide by.
The equivalent fraction has the number and unit before the per
divided by the implied number (1) and the unit after the per. | Equivalent fraction: |
Other examples of translating words to a fraction are given below.
Inverse fraction | Statement in words | Fraction equivalent to statement in words |
| 1000 g per kg | | |
| 109 nm per m | | |
Each of these
fractions is
equivalent to its
inverse.
This is because the numerator and denominator of each fraction are equivalent (each expression is actually equal to 1).
Both of the
fractions in any row can be used as
conversion factors,
in one case from the larger to the smaller unit, and in the other from the smaller to the larger unit.
The appropriate conversion factor has the
desired unit in the numerator and the
given unit in the denominator.
When this is multiplied by the given number and given unit, the
given unit cancels as shown for conversion of g to kg.
Understanding how to write conversion factors and how to apply these is a useful skill for many areas of chemistry.