Without performing long division,state whethe | vedclass

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

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Terminating

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(A) To determine if the decimal expansion of a rational number $\frac{p}{q}$ is terminating,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 $\frac{13}{3125}$,the denominator is $q = 3125$.Prime factorization of $3125 = 5 	imes 5 	imes 5 	imes 5 	imes 5 = 5^5$.This can be written as $2^0 	imes 5^5$.Since the denominator is in the form $2^n 	imes 5^m$ (where $n=0$ and $m=5$),the decimal expansion of $\frac{13}{3125}$ is terminating.

Without performing long division,state whether the decimal expansion of the rational number $\frac{13}{3125}$ is terminating or non-terminating repeating.

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