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Decimal expansion

  1. Sep 13, 2013 #1
    1. The problem statement, all variables and given/known data
    How many decimal expansions terminate in an infinite string of 9's?
    How many dont?
    3. The attempt at a solution
    If we have a number terminate with an infinite amount of 9's then it will be a rational number.
    So there would be countably many of these.

    And since irrational numbers do not end with all 9's then their would be
    uncountably many of them that do not.
     
  2. jcsd
  3. Sep 13, 2013 #2

    Zondrina

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    Homework Helper

    That's the right idea.
     
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