Question

without actually performing the long division state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion 13 upon 3125

Answer 1

13 upon 3125 is a non terminating decimal because 3125 has only 5 as its factor

Answer 2

A rational number's decimal expansion can be terminating only if the prime factors of the denominator consist of both 2s and 5s (but nothing else than that).

But the prime factorisation of 3125 is 5×5×5×5×5.

As the prime factorisation contains only 5s and not even a single 2, we conclude that 13/3125 has a non-terminating decimal expansion.