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Something in my brain has gone horribly wrong

  1. Oct 26, 2007 #1
    This is an extremely easy concept that for some reason is destroying my life right now.

    It just came up in a physics problem that I posted elsewhere.

    I have a cube of side length .6m So the area of one side is (.6)^2=
    .36m^2

    This does not agree with me. If it were of side length 6 then A=6^2=36.

    This makes sense. 36>6. But .36<.6

    Same with volume 6^3=216>6........but .6^3=.216<.6

    what gives? What the hell is wrong with me/this?

    Casey
     
  2. jcsd
  3. Oct 26, 2007 #2

    cristo

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    It's just the units that you're using. If you think of a cube of sides 60cm, then the area of one side would be 3600cm^2. Now, converting into metres; 1m^2=(100cm)*(100cm)=10,000cm^2, so 3600cm^2=3600/10000 m^2=0.36m^2.
     
  4. Oct 26, 2007 #3
    Maybe I need to sleep on it, but I still don't see how the number of units squared can be less than the number of units in 1 dimension.
     
  5. Oct 26, 2007 #4
    ....maybe I see it now...darn, now I have NO idea what is wrong in my physics problem:yuck:

    Casey
     
  6. Oct 26, 2007 #5

    Gokul43201

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    It seems your question can be reduced to a problem with accepting that for all positive n, n > 1 => n2 > n and n < 1 => n2 < n.

    Does restating your confusion in the above terms help clear some fog?
     
  7. Oct 27, 2007 #6

    Integral

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    You are trying to compare .6m a length to .36m2 an area. This is an apples to oranges comparison, there is no way that a length can be greater then, less then, or even equal to a length.

    If you would take the time to draw a picture, I bet you will quickly agree that square .6m on a side is about 1/3 of a square 1m on a side.
     
    Last edited: Oct 27, 2007
  8. Oct 27, 2007 #7

    Gib Z

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    Remember, when you square it, your units also get squared. So basically before when it only took 100 cm for 1 m, now it takes 10,000 cm^2 for 1m^2.
     
  9. Oct 27, 2007 #8
    Yeah. I kid got beef with that too. I am not sure why yet...but I do.



    Did I just say got beef?

    Casey
     
  10. Oct 27, 2007 #9

    arildno

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    Dearly Missed

    Multiplying a number with another number that is less than 1 yields a number less than the first.
     
  11. Oct 27, 2007 #10

    HallsofIvy

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    Have you looked at a graph of y= x2 lately? For x< 1, it is below the line y= x. For x> 1, it is above. Of course, the curve and line cross at (0,0) and (1,1).
     
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