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(A) 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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Terminating decimal expansion

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(A) To determine if a rational number $\frac{p}{q}$ has a terminating decimal expansion,we check the prime factorization of the denominator $q$.If $q$ is of the form $2^{m} 	imes 5^{n}$,where $m$ and $n$ are non-negative integers,then the decimal expansion is terminating.Given fraction: $\frac{15}{1600}$.First,simplify the fraction: $\frac{15}{1600} = \frac{3}{320}$.Now,find the prime factorization of the denominator $320$:$320 = 32 	imes 10 = 2^{5} 	imes 2 	imes 5 = 2^{6} 	imes 5^{1}$.Since the denominator is in the form $2^{m} 	imes 5^{n}$ (where $m=6$ and $n=1$),the decimal expansion of $\frac{15}{1600}$ is terminating.

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: $\frac{15}{1600}$.

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