How can you convert centimeters to millimeters?

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.