State whether the following rational number h | vedclass

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(A) rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of the denominator $q$ is of the form $2^n 	imes 5^m

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Terminating

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(A) rational number $\frac{p}{q}$ has a terminating decimal expansion if the prime factorization of the denominator $q$ is of the form $2^n 	imes 5^m$,where $n$ and $m$ are non-negative integers.Here,the denominator is $8 = 2^3 = 2^3 	imes 5^0$.Since the denominator is in the form $2^n 	imes 5^m$,the rational number $\frac{17}{8}$ has a terminating decimal expansion.To find the decimal expansion: $\frac{17}{8} = \frac{17 	imes 125}{8 	imes 125} = \frac{2125}{1000} = 2.125$.

State whether the following rational number has a terminating decimal expansion or not. If it has a terminating decimal expansion,find it: $\frac{17}{8}$

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