Question

Without actual division, find which of the following rational numbers are terminating decimals:

$\frac{17}{125}$

Answer 1

$\frac{17}{125}$ is the given rational number.

A rational number $\frac{p}{q},(q\ne 0)$ is a terminating decimal if the prime factors of $q$ are $2$ and $5$ only.

Here,$\frac{17}{125}$ has denominator $125$.

$125=5^3$

$\Rightarrow 125$ has no prime factor other than $5$.

Hence, $\frac{17}{125}$ is a terminating decimal.