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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 t

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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 the denominator $q$ is of the form $2^{m} 	imes 5^{n}$,where $m$ and $n$ are non-negative integers,then the rational number has a terminating decimal expansion.In the given expression $\frac{23}{2^{3} 	imes 5^{2}}$,the denominator is $2^{3} 	imes 5^{2}$.Here,$m = 3$ and $n = 2$,which are non-negative integers.Since the denominator is in the form $2^{m} 	imes 5^{n}$,the rational number $\frac{23}{2^{3} 	imes 5^{2}}$ has a terminating decimal expansion.

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: $\frac{23}{2^{3} \times 5^{2}}$

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