# When should I be converting to units?

## Main Question or Discussion Point

I am new to the forum, and I am sure it will be evident by this first question, but I hope to learn a lot here.

so.. here is what I was thinking about that prompted me to look for a math forum. Say I have (20cm)2. That would be 400 square centimeters, or, 4 square meters? Now, what if I convert to meters before squaring? Then, I have (0.2 m)2, or .04 square meters... 4 square centimeters? Why does this not work? When should I be converting to units? Before or after multiplication.

Thanks for any input.

mezarashi
Homework Helper
That is because you are making wrong analogies. You need to start with definitions you know for sure. As defined, you have:

100cm = 1 meter.
If you have 0.2 meters, how many cm do you have?

Now squaring both sides you have:

10000cm^2 = 1 meter^2.

If 1 square meter is 10000 square cm, then how many square cm is 0.04 square meters?

HallsofIvy
Homework Helper
silverdiesel said:
I am new to the forum, and I am sure it will be evident by this first question, but I hope to learn a lot here.
so.. here is what I was thinking about that prompted me to look for a math forum. Say I have (20cm)2. That would be 400 square centimeters, or, 4 square meters? Now, what if I convert to meters before squaring? Then, I have (0.2 m)2, or .04 square meters... 4 square centimeters? Why does this not work? When should I be converting to units? Before or after multiplication.
Thanks for any input.

A meter is 100 cm but a square meter is not 100 square cm! In fact, a square meter is (100)2= 10000 square cm.

(20 cm)2= 400 square cm = 400/10000= 0.04 square meters, exactly as if you had squared (0.2 m)2= 0.04 square meters.

Ah, perfect. I knew there was somthing very simple I was missing.
Thank you.:tongue2: