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.
$\frac{64}{455}$

Answer 1

We have

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

Clearly $455$ is not of the form $2^m\times 5^n$

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

$\Rightarrow \frac{64}{455}$ is non -terminating repeating.