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I was wondering if a rational number p/q can be identified as either repeating decimal or terminating decimal by looking at numerator and denominator. In other words, is there a property that if p and q follow, then p/q is always repeating decimal.

Amardeep reddy
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    If it terminates, it means that multiplying it by a large enough power of $10$ it becomes integer. That means that the denominator should be a product of a power of $2$ and $5$ only. –  Apr 04 '18 at 03:33

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To terminate you must have $\frac pq=\frac a{10^n}$ for some $n$. As $10^n$ has only $2$ and $5$ for prime factors, so must $q$.

Ross Millikan
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