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Orders of magnitude help

  1. Mar 25, 2014 #1
    1. The problem statement, all variables and given/known data
    Hi guys this isn't so much a coursework or homework help problem but figured this would be a sensible place to post my question. Basically I got back an assignment I had recently completed from my tutor and I had been marked down for some errors in regard to the orders of magnitude and he said I have been using the same order of magnitude for lets say μm (10^-6) as μm^2. My question is, what is the difference when the units are squared? Does this mean that, lets say 8μm^2 would not be equal to 8x10^-6 but a different value? Any help is appreciated to clear this up :redface:
     
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  3. Mar 25, 2014 #2

    jbunniii

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    Consider a square with side lengths equal to ##1 \mu m = 10^{-6}m##. Try expressing the area of this square in ##\mu m^2## and in ##m^2##.
     
  4. Mar 25, 2014 #3
    Would this be correct:

    For area in μm = 1μm^2

    and area in m = 10^-6m^2

    Thanks for replying!
     
  5. Mar 25, 2014 #4

    jbunniii

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    Yes.

    No. If the side length is ##10^{-6}m##, then what do you get when you square that? Surely the square of ##10^{-6}## is not ##10^{-6}##.
     
  6. Mar 25, 2014 #5
    Ah I see! It would be 10^-12?
     
  7. Mar 25, 2014 #6
    The conversion factor must also be squared - obviously. Draw a square 10cm by side on a piece of paper. Cut it down to squares 1cm by 1 cm (Don't really cut, just draw them). How many little squares do you have at hand? Do you have only 10 little squares?
     
  8. Mar 25, 2014 #7

    jbunniii

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    That's right. So ##1 \mu m^2 = 10^{-12} m^2##, not ##10^{-6}m^2##.
     
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