Question

Without actually dividing find if $3.12\overline{7}$ is terminating decimal.

Answer 1

Given fraction $\frac{3}{25}$

The $\frac{p}{q}$ is terminating decimal if

(i) p & q are co-prime and

(ii) q is in the form $2^n{5}^m$

Here 3 and 25 are co-prime

And $25=2^0\times 5^2$

So $\frac{3}{25}$ is terminating decimal (yes)