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

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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 check 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 fraction $\frac{13}{3125}$,the denominator is $3125$.Prime factorization of $3125 = 5 	imes 5 	imes 5 	imes 5 	imes 5 = 5^5$.This can be written as $2^0 	imes 5^5$,which is in the form $2^n 	imes 5^m$ (where $n=0$ and $m=5$).Since the denominator is of the form $2^n 	imes 5^m$,the decimal expansion of $\frac{13}{3125}$ 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: $\frac{13}{3125}$.

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