Question

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

Answer 1

Let,

$\frac{6}{15}=\frac{2}{5}$

Checking co-prime

$2$ and $5$ are no factor

Therefore $2$ and $5$ are co prime

For denominator $=5=2^0\times 5^1$

in the form of $2^n{5}^m$ where $m=1,n=0$

Hence they are terminating decimal