Question

Without actually dividing find if $\frac{11}{18}$ is terminating decimal.

Answer 1

Given, $\frac{11}{18}$.

The rational number $\frac{p}{q}$ is terminating if

(i) $p$ and $q$ are co-prime and

(ii) $q$ is of the form $2^n{5}^m$, where $n,m$ are non-negative.

In $\frac{11}{18}$,

The denominator $18=3^2\times 2$, is not from of $2^n{5}^m$

Hence, without actual division, $\frac{11}{18}$ is not a terminating decimal.