When should I be converting to units?

[silverdiesel]

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]

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]

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.

 

[silverdiesel]

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