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Are all rational numbers normal?

  1. Nov 17, 2014 #1
  2. jcsd
  3. Nov 17, 2014 #2


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    On the contrary, NO rational numbers are normal! I think you have a wrong idea of what a "normal number" is. A "normal number" is one such that all possible strings of digits, n digits long, occur an equal number of times. A rational number is always eventually repeating (thinking of a terminating decimal as "repeating" 0s).

    The number you give is a terminating decimal with 20 digits. It contains NO strings of length 21 or higher!
  4. Nov 17, 2014 #3


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    He means ##0.\overline{0123456789}##, not a terminating decimal but still not normal.
  5. Nov 17, 2014 #4
    Ah, I looked at the definition more closely and now I see my misunderstanding. It must be any string of any length, not simply a digit. But this is a simply normal number, is that correct?
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