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When should I be converting to units?

  1. Dec 16, 2005 #1
    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.
  2. jcsd
  3. Dec 16, 2005 #2


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    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?
  4. Dec 16, 2005 #3


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    Staff Emeritus
    Science Advisor

    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.
  5. Dec 16, 2005 #4
    Ah, perfect. I knew there was somthing very simple I was missing.
    Thank you.:tongue2:
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