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Inequality with modulus question

  1. Jun 30, 2012 #1
    1. The problem statement, all variables and given/known data

    What is the maximum value of 'n' such that the modulus of pi-22/7 < 10-n?

    2. Relevant equations



    3. The attempt at a solution

    I have worked out that pi > -10-n + 22/7 , and pi < 10n +22/7. I also know that 10-n is equivalent to 1/10n. I do not know where to go after this however.
     
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  3. Jun 30, 2012 #2

    tiny-tim

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    hi vodkasoup! :smile:
    π = 3.14159265…

    22/7 = 3.14285714…​

    what is π - 22/7 ?

    what is it less than? :wink:
     
  4. Jun 30, 2012 #3
    Hi tiny-tim, thanks for the reply :)

    Haha, I didn't even notice the 22/7 relating to pi!

    So π - 22/7 is, according to my calculator, -0.001 .... which is less than 0.

    I still can't quite see how to relate this to 10-n. I'm a bit slow today, haha.

    It seems that no matter how much I increase the value of n, -0.001 will always be lower.

    Am I on the right track with the 1/10n thing?
     
  5. Jun 30, 2012 #4

    tiny-tim

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    hi vodkasoup! :smile:
    that's ok, the question asks you about the modulus, doesn't it? :wink:
    what's 10-1? what's 10-2? what's 10-3? …
     
  6. Jun 30, 2012 #5
    Hmm. I think I may be a bit unclear on the meaning of 'modulus'. Is it the 'distance' to 0 of a given point?

    If that is so, would the maximum value of n be 2, because 1 / 10 to the third power is 0.001, which does not satisfy the inequality?
     
  7. Jun 30, 2012 #6

    tiny-tim

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    yes, modulus is the magnitude

    so, for a number x, the modulus, |x|, is always positive (or zero)
    yes :smile:
     
  8. Jul 2, 2012 #7
    Thanks so much for your help tiny-tim! Sorry I took so long to reply here; I've been so busy over the last couple of days. Very much appreciate your help.
     
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