Look at several examples of rational numbers in the form $\frac{p}{q} (q \neq 0),$ 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?

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Solution

Prime factorization is the process of finding which prime numbers you need to multiply together to get a certain number. So prime factorization of denominators (q) must have only the power of 2 or 5 or both.

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