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Question

(A) First,simplify the fraction to its lowest terms:$\frac{6}{15} = \frac{2 	imes 3}{5 	imes 3} = \frac{2}{5}$$A$ rational number $\frac{p}{q}$ has

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Terminating decimal expansion

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(A) First,simplify the fraction to its lowest terms:$\frac{6}{15} = \frac{2 	imes 3}{5 	imes 3} = \frac{2}{5}$$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 $5$,which can be written as $2^0 	imes 5^1$.Since the denominator is in the form $2^n 	imes 5^m$,the decimal expansion of $\frac{6}{15}$ 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: $\frac{6}{15}$

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