Question

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

Answer 1

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Answer 2

$\sf \underline\red{Solution:}$

The decimal representation will be terminating, if the denominators have factors 2 or 5 or both.

Therefore, p/q is a terminating decimal, when prime factorization of q must have only powers of 2 or 5 or both.