Given any fraction where both the numerator (N) and denominator (D) are both positive and are both whole numbers.
Without manually dividing N by D, is it possible to pre-determine if the resulting value represented in decimal would be a repeating value? (e.g. 44÷33 is 1.3333333333....)
I believe the value of N ÷ D will NOT be a repeating decimal if and only if D is any of the following
- D is equal to 1 OR
- D's prime factors only consist of 2's and/or 5's. (includes all multiples of 10)
Otherwise, if none of the two rules above hold true, then the positive whole numbers N and D will divide into repeating decimal.
Correct, or am I missing a case?