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Reciprocals and repeating digits

  1. Oct 27, 2013 #1
    So when you take the reciprocals of integers, some have nice non repeating decimal forms like 0.5 and 0.2, but of course a lot of them give infinite repeating strings.

    1/7 gives 0.142857 repeating, so there are 6 digits repeating.
    1/12 give 0.083333... but there is only 1 digits that's repeating, which is 3.

    Which integer reciprocal gives the most digits repeating? Or is there no answer?
  2. jcsd
  3. Oct 28, 2013 #2


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    Consider the sequence ##\frac19, \frac{1}{99}, \frac{1}{999}, \frac{1}{9999},\ldots##
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