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

We observe that when q is 2, 4, 5, 8, 10… then the decimal expansion is terminating. For example:

1/2 = 0.5͞, denominator q = 2^{1}

7/8 = 0.͞8͞7͞5, denominator q = 2^{3}

4/5 = 0.8͞, denominator q = 5^{1}

It can be observed that the terminating decimal can be obtained in a condition where prime factorization of the denominator of the given fractions has the power of 2 only or 5 only or both.

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