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For simple fraction, we can easily convert it to repeating decimal by calculator. Ex. $\frac 1 3 = 0.33333\ldots$, $\frac 1 7=0.(142857),\ldots$ But some fraction fraction like $10/29, 1/97,...$ The repeating part of them are too long, so it can't fully show on the calculator. So is there any algorithm to find the repeating part for that fraction?

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  • $\begingroup$ Doing the division by hand until finding the first repeated remainder. The repeating part can be arbitrarily long and appear after an arbitrarily long initial part, so every computer capacity can be exceeded. $\endgroup$ – egreg Mar 22 '15 at 13:45
  • $\begingroup$ Possible duplicate of Convert a fraction to infinite repeating decimal? $\endgroup$ – David K Jul 25 '18 at 12:40
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Yes, there is. This wikipedia page explains the various algorithms in the Section "Converting repeating decimals to fractions".

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