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QUESTION

How can you convert centimeters to millimeters?

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.