# Question #feca2

Sep 7, 2014

In order to convert from one unit to another, you must know the appropriate equalities in order to determine the appropriate conversion factors, and then use dimensional analysis to make the conversion.

To convert $\text{2ft", "6in}$ to millimeters, do the following:

1. Convert feet to inches.
Equality between feet and inches: $\text{1ft}$ = $\text{12in}$

The conversion factors are $\text{1ft"/"12in}$ and $\text{12in"/"1ft}$. Multiply the given measurement times the conversion factor that will cancel the feet. Another way to think of it is that you multiply times the conversion factor that has the desired unit, in this case inches, on top.

$\text{2ft}$ x $\text{12in"/"1ft}$ = $\text{24in}$

The feet cancel, leaving inches.

$\text{24in}$ + $\text{6in}$ = $\text{30in}$.

3. Convert inches to centimeters.
Equality between centimeters and inches: $\text{2.54cm" = "1in}$

The conversion factors are $\text{2.54cm"/"1in}$ and $\text{1in"/"2.54cm}$

$\text{30in}$ x $\text{2.54cm"/"1in}$ = $\text{76.2cm}$

The inches cancel, leaving centimeters.

4. Convert centimeters to millimeters.
Equality between centimeters and millimeters: $\text{1cm}$ = $\text{10mm}$

The conversion factors are $\text{1cm"/"10mm}$ and $\text{10mm"/"1cm}$

$\text{76.2cm}$ x $\text{10mm"/"1cm}$ = $\text{762mm}$

The centimeters cancel, leaving millimeters.