Determine whether the rational number frac{64 | vedclass

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(B) 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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Non-terminating repeating

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(B) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check the prime factorization of the denominator $q$.If $q = 2^n 	imes 5^m$,where $n$ and $m$ are non-negative integers,the decimal expansion is terminating.Here,$q = 455$.Prime factorization of $455 = 5 	imes 7 	imes 13$.Since the prime factorization contains factors other than $2$ and $5$ (specifically $7$ and $13$),the decimal expansion of $\frac{64}{455}$ is non-terminating repeating.

Determine whether the rational number $\frac{64}{455}$ has a terminating or non-terminating repeating decimal expansion. If it is terminating,write down its decimal expansion.

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