# Unit conversion not coming out right.

I'm trying to convert 20.7x10^(-4)m^2 to inches^2. And after that's done use it to figure the price at 3.25/lb^2. The answer is supposed to be $10.43. I have the conversion factor 1m = 39.37in. I've tried 20.7x10^(-4) x 39.37, then that times the 3.25. I tried converting that to inches, cubing it and then x 3.25, and a couple other things. I know I've done this before but I can't kind the scrap sheet I did it on and can't figure out what I did here last time. ## 2 Answers To convert from square metres to square inches, we multiply by$(39.37)^2$. An example with simpler numbers may help. Recall that a foot is$12$inches. A$1$foot by$1$foot cardboard square can be divided into$1441$inch by$1$inch squares, so it has area$(12)^2$square inches. Thus$1$square foot is$(12)^2$square inches. • Wow have I been over thinking that. Thanks... – windy401 Sep 6 '14 at 0:54 • You are welcome. You will find that when you calculate using$(39.37)^2$, you will get about$10.4276\$, which, rounded to two decimal places, is the answer you are looking for. – André Nicolas Sep 6 '14 at 0:57

You have to do the following:

$$x=20.7\cdot10^{-4}\text{m}^2=\Big(\frac{39.37 \text{ in}}{1 \text{ m}}\Big)^2$$

That's equal to :

$$x=20.7\cdot10^{-4}\text{m}^2=\frac{39.37^2 \text{ in}^2}{1 \text{ m}^2}$$

The meter squared just cancel and you get:

$$x=20.7\cdot10^{-4}\cdot 39.37^2 \text{ in}^2$$

I recommend this method in order to do unit conversion.