Question

How can you convert centimeters to millimeters?

Answer 1

Quick Answer: Multiply by 10.

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

In this case,

`"100 cm" = "1 m"` and `"1000 mm" = "1 m"`

Therefore

`"100 cm" = "1000 mm"` or `"1 cm" = "10 mm"`

This gives you two conversion factors:

`"1 cm"/"10 mm"` and `"10 mm"/"1 cm"`

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

`"1 cm"/"10 mm"` = `"10 mm"/"1 cm" = 1`

EXAMPLE

Convert 3.1 cm into millimetres.

You multiply by a conversion factor: `"1 cm"/"10 mm"` or `"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

`"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 `"1 cm" = "10 mm"`, you can always use the definitions of milli and centi:

`"milli" = 10^-3`; so `"1 mm" = 10^-3 "m"`
`"centi "= 10^-2`, so `"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.