Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{6}{15}$

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Solution

On simplifying the fraction, the denominator is 5.

Therefore, denominator is of the form $2^{n} {.5}^{m}$ , where m=1 and n=0.
It means rational number $\frac{6}{15}$ has terminating decimal expansion.

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{129}{2^{2} {.5}^{7} {.7}^{5}}$

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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : 615

On simplifying the fraction, the denominator is 5. Therefore, denominator is of the form 2n.5m, where m=1 and n=0. It means rational number 615 has terminating decimal expansion.

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{6}{15}$

On simplifying the fraction, the denominator is 5.

Therefore, denominator is of the form $2^{n} {.5}^{m}$ , where m=1 and n=0.
It means rational number $\frac{6}{15}$ has terminating decimal expansion.