Question

Without actual division, check whether $\frac{47}{14}$ is terminating or not.

Answer 1

If the denominator can be in the powers of either $2$ or $5$ or both, then it will be a terminating decimal, otherwise non-terminating.

But the denominator of the given fraction is $14$ and $14$ can be rewritten as $2\times 7$, i.e. not in the form $2^m\times 5^n$; where $n,m$ are non-negative.

Hence, the rational number is non-terminating.