Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates.

Foundation

Mathematics Foundation

HCF and LCM

Recurring Decimal Number

Linear Equations in One Variable

Question

Without actually performing the long division, state whether the following rational number will have terminating decimal expansion or a non-terminating repeating decimal expansion. Also, find the numbers of places of decimals after which the decimal expansion terminates. $\frac{64}{455}$

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We have

\frac{64}{455} = \frac{64}{5 \times 7 \times 13}

Clearly 455 is not of the form 2^m× 5ⁿ

If it is not of the above mentioned form then, the decimal expansion is non-terminating

\Rightarrow \frac{64}{455}

is non -terminating repeating.