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(A) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we examine the prime factorization of the denominator $q$.If $

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Terminating decimal expansion

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(A) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we examine the prime factorization of the denominator $q$.If $q$ is of the form $2^n 	imes 5^m$,where $n$ and $m$ are non-negative integers,then the decimal expansion is terminating.Given the rational number $\frac{17}{8}$.The denominator is $8$.Prime factorization of $8 = 2 	imes 2 	imes 2 = 2^3$.We can write $8 = 2^3 	imes 5^0$.Since the denominator is of the form $2^n 	imes 5^m$,the decimal expansion of $\frac{17}{8}$ is terminating.

Without actually performing the long division,state whether the following rational number will have a terminating decimal expansion or a non-terminating repeating decimal expansion: $\frac{17}{8}$.

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