fraction-to-recurring-decimal

Simulating division on paper

Pic from Wikipedia

           .  .
        0.0675
        _______
   74 ) 5.00000
        4.44
        _______
          560
          518
          _____
           420
           370
           ____
            500

When to stop?

Have a look at at the pic above, when we see 500 we are sure that the next quotient is 6. Because we had calculated 500 / 74 before.

What we need is to remember and check if the quotient has been done once before.