How can you convert centimeters to millimeters?

Question

45024 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2014-01-14T18:06:49

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.

![facweb.bhc.edu)