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Rational and Irrational

  1. Apr 13, 2008 #1
    Can someone pls help me on "rational and Irrational numbers". Esp. on Decimals. I cant classify if it is rational or irrational.
     
  2. jcsd
  3. Apr 13, 2008 #2

    nicksauce

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    If you can write z = x/y where x and y are integers, then z is rational. Otherwise z is irrational.
     
  4. Apr 13, 2008 #3
    is pi rational?
     
  5. Apr 13, 2008 #4
    is .66666..... rational? why?
     
  6. Apr 13, 2008 #5

    nicksauce

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    Is Pi rational? No. Not sure how to prove it though.
    Is .66666.... rational? Can you think of a fraction that gives .666666... ? I would hope you can.
     
  7. Apr 13, 2008 #6
    ok, thanks nicksauce
     
  8. Apr 13, 2008 #7

    lurflurf

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    for decimal form a useful fact is
    a real nummber x is rational if and only if its decimal expansion at some point repeats.
    let () be repeat this sequence
    1/9=.(1) so rational
    8134808921309.2872918752801(29148991280409) so rational

    pi has no such patern, though this is not obvious
     
  9. Apr 13, 2008 #8
  10. Apr 14, 2008 #9
    Little off-topic, but here goes: I'm curious, is this not true in some integer base?
     
  11. Apr 15, 2008 #10

    HallsofIvy

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    If you mean "is it true in any integer base", yes.
     
  12. Apr 15, 2008 #11
    The question has been answered, but maybe I can help you grasp this a little easier. "Irrational" means that it cannot be expressed as a ratio (NOT that it is 'irrational' in the sense of not being reasonable.) Hence "irrational," or "un-ratio-expressable" if you will. A rational number, on the other hand, CAN be expressed as a ratio. It's "rational," or "ratio-expressable." Since a repeating decimal is given by the 'ratio' of two numbers, it is indeed rational (i.e. 'expressable as a ratio.')
     
  13. Apr 15, 2008 #12

    lurflurf

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    Sorry no
    in base pi
    pi which is irrational=10
    4 which is rational=10.220122021

    a problem with algebraic bases
    in base root-2
    root 2=10
    2=100
     
  14. Apr 21, 2008 #13

    HallsofIvy

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    Did you miss the word "integer" in "integer base"?
     
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