Question

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

$\frac{5}{12}$

Answer 1

$\frac{5}{12}$ is the given rational number.

We know that 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,$\frac{5}{12}$ has denominator $12$.

And $12=2\times 2\times 3$

$\Rightarrow 12$ has a prime factor $3$, other than $2$ and $5$.

Hence, $\frac{5}{12}$ is not a terminating decimal.