# How can you convert centimeters to millimeters?

Jan 14, 2014

To do any conversion, you find the relationship between the two units.

In this case,

$\text{100 cm" = "1 m}$ and $\text{1000 mm" = "1 m}$

Therefore

$\text{100 cm" = "1000 mm}$ or $\text{1 cm" = "10 mm}$

This gives you two conversion factors:

$\text{1 cm"/"10 mm}$ and $\text{10 mm"/"1 cm}$

and if you look at the equation, you'll see that

$\text{1 cm"/"10 mm}$ = $\text{10 mm"/"1 cm} = 1$

EXAMPLE

Convert 3.1 cm into millimetres.

You multiply by a conversion factor: $\text{1 cm"/"10 mm}$ or $\text{10 mm"/"1 cm}$.

Choose the one that gives you the correct units for the answer.

3.1 cancel("cm") × "10 mm"/(1 cancel("cm")) =" 31 mm"

Note that the "cm" cancels out and leaves you with the answer in “mm”. If you had chosen the other conversion factor, you would have gotten

$\text{3.1 cm" × "1 cm"/"10 mm" = "0.31 cm"^2"/mm}$

The strange units for the answer tell you that you have made a mistake.

LAST RESORT

If you can’t remember that $\text{1 cm" = "10 mm}$, you can always use the definitions of milli and centi:

$\text{milli} = {10}^{-} 3$; so $\text{1 mm" = 10^-3 "m}$
$\text{centi } = {10}^{-} 2$, so $\text{1 cm" = 10^-2 "m}$

Then you can convert “cm” to “m” and “m” to “mm”.

3.1 cancel("cm") × (10^(-2) cancel("m"))/(1 cancel("cm")) × "1 mm"/(10^(-3) cancel("m")) = "31 mm"

It's an extra step, but it always works.