Look at several examples of rational numbers in the form (q 0), where p and q are integers with no common factors other than 1 and having terminating, decimal representations. Can you guess what property q must satisfy?

A rational number is a terminating decimal only, when prime factors of q are 2 and 5 only. Therefore, is a terminating decimal only, when prime factorisation of q must have only powers of 2 or 5 or both.


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