Question

Without actually performing long division method, find if the rational number will have terminating or non-terminating repeating decimal expansion.


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Answer 1

Answer:

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