Display illimited rational number defined by two integer

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I'm working on a Rational number class in c++. The Rational number is defined by two int (numerator and denominator). I would like to display it properly as digit number. for now, I determine if the number is an "illimited" or a limited digit rational number.

Here is a little pseudo code to illustrate:

define print_rational(num, denom):
   if(isUnlimited(num, denom):
       ?
   else:
       //"limited" rational, no problem for them

I would like to display illimited numbers like this : print one time the repetitives digits, then "..." (Example : 1/3 -> 0.3..., 1/11 -> 0.09...)

So, is there an algorithm to find the block of digit who will be repeat in a rational number ?

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Convert your result into string and then apply Longest repeated substring problem to it.