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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 in 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 in the form $2^{m} 	imes 5^{n}$,where $m$ and $n$ are non-negative integers.Given the rational number $\frac{29}{343}$:The denominator is $343$.Prime factorization of $343 = 7 	imes 7 	imes 7 = 7^{3}$.Since the prime factorization of the denominator is $7^{3}$,which is not in the form $2^{m} 	imes 5^{n}$,the decimal expansion of $\frac{29}{343}$ 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: $\frac{29}{343}$.

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Write down the decimal expansion of the rational number $\frac{129}{2^{2} 5^{7} 7^{5}}$.

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