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

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Terminating decimal expansion

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(A) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check if the prime factorization of the denominator $q$ is of the form $2^{m} 	imes 5^{n}$,where $m$ and $n$ are non-negative integers.Given the rational number $\frac{35}{50}$,we first simplify it to its lowest form:$\frac{35}{50} = \frac{7 	imes 5}{10 	imes 5} = \frac{7}{10}$.The denominator is $10$.The prime factorization of $10$ is $2^{1} 	imes 5^{1}$.Since the denominator is of the form $2^{m} 	imes 5^{n}$ (where $m=1$ and $n=1$),the rational number $\frac{35}{50}$ has a terminating decimal expansion.

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: $\frac{35}{50}$.

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