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.999 = 1?

  1. Oct 25, 2005 #1
    Elaborate.
    Plus, wouldn't that mean 1.999...8 = 2?
     
  2. jcsd
  3. Oct 25, 2005 #2
  4. Oct 25, 2005 #3

    Lisa!

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    Gold Member

    God! Again this question. :cry:
     
  5. Oct 26, 2005 #4

    HallsofIvy

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    By definition of a "base 10 numeration system", 0.999... means the limit of the sequence 0.9, 0.99, 0.999, 0.9999, ...
    Those are the partial sums of a geometric series (a+ ar+ ar2+ ...) with a= 0.9 and r= 0.1. It's easy to show that a geometric series converges to a/(1-r) which in this case is 0.9/(1- 0.1)= 0.9/0.9= 1.
    For the second question, what do you mean by "1.999...8"? If that ... indicates an infinite string then there is no end to put the 8 on! If you mean the limit of the sequence 1.8, 1.98, 1.998, 1.9998, ... (that's what 1.999... means- without the 8 of course) then it is equal to 2, yes.
     
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