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Basic Dimensional Analysis Question

  1. Sep 5, 2011 #1
    1. Convert 1.2 in^2 to cm^2



    2. 1 CM = 10^-2 and 1 inch = 2.54 centimeteres



    3. The attempt at a solution

    Can't we just do 1.2*2.54=3.048 and write that as our answer?
     
  2. jcsd
  3. Sep 5, 2011 #2

    lewando

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    You could, but it would be wrong. :smile:

    If 1 in = 2.54 cm, then, squaring both sides, 12 in2 = 2.542 cm2.

    or simplified: 1 in2 = 6.4516 cm2. From this, we get the following facts:

    1 = (1 in2) / (6.4516 cm2)

    1 = (6.4516 cm2) / (1 in2)

    Remember, you can multiply anything by 1 and it will not alter the value you are trying to convert. If you are starting with a value that has units of in2 (as you are) then multiply that value by the ratio of the second equation (that ratio is equal to 1). The in2 will cancel out leaving you with cm2 in the numerator (which is what you want).

    1.2 [STRIKE]in2[/STRIKE] * (6.4516 cm2) / (1 [STRIKE]in2[/STRIKE])
     
  4. Sep 5, 2011 #3

    tiny-tim

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    hi lolzwhut?! :smile:
    it's square inches! :wink:
     
  5. Sep 5, 2011 #4

    Borek

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    Staff: Mentor

    To add to what lewando wrote - if you were not ignoring units, you would see that it is wrong.

    Trying shortcuts when you don't understand what you are doing rarely works. Dimensional analysis strength relies on the fact that it not only gives correct results, but also gives signals if you get lost. However, it works only when you use both numbers and units in conversion coefficients.
     
  6. Sep 5, 2011 #5

    HallsofIvy

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    Your first error is here. 1 cm= 10^-2 what?

    And, as others have pointed out, you simply dropped the units here and the units are the whole point of the problem.
     
  7. Sep 5, 2011 #6
    Wow, so 7.74 cm^2 is what I'm getting.

    Thanks for the help guys. I definitely won't forget my units this time xD But yeah, I got 7.74 cm^2.
     
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