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(B) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,the prime factorization of the denominator $q$ must be of the

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Non-terminating repeating decimal expansion

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(B) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,the prime factorization of the denominator $q$ must be of the form $2^{m} 	imes 5^{n}$,where $m$ and $n$ are non-negative integers.Given the rational number $\frac{64}{455}$.First,find the prime factorization of the denominator $455$:$455 = 5 	imes 7 	imes 13$.Since the prime factorization of the denominator $455$ contains factors other than $2$ and $5$ (specifically $7$ and $13$),the rational number $\frac{64}{455}$ does not have a terminating decimal expansion.Therefore,the decimal expansion of $\frac{64}{455}$ is non-terminating repeating.

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: $\frac{64}{455}$.

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