Unit conversion not coming out right.

Question

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.

Answer 1

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 $144$ $1$ inch by $1$ inch squares, so it has area $(12)^2$ square inches. Thus $1$ square foot is $(12)^2$ square inches.

Answer 2

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.