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.
$\frac{29}{343}$

Answer 1

Given fraction can be rewritten as,

$\frac{29}{343}=\frac{29}{7^3}$

Clearly $343$ is not of the form $2^m\times 5^n.$

Therefore the decimal expansion of $\frac{29}{343}$ is non -terminating repeating.