The decimal expansion of frac{13}{3125} is: | vedclass

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

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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 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,the decimal expansion is terminating.Here,$q = 3125$.$3125 = 5 	imes 5 	imes 5 	imes 5 	imes 5 = 5^5$.Since $3125$ can be written as $2^0 	imes 5^5$,it satisfies the condition $2^n 	imes 5^m$.Therefore,the decimal expansion of $\frac{13}{3125}$ is terminating.

The decimal expansion of $\frac{13}{3125}$ is:

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