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.
