# Examine whether

Question:

Examine whether $\frac{17}{30}$ is a terminating decimal.

Solution:

$\frac{17}{30}=\frac{17}{2 \times 3 \times 5}$

We know that 2, 3 and 5 are not the factors of 17.

So, $\frac{17}{30}$ is in its simplest form.

Also, $30=2 \times 3 \times 5 \neq\left(2^{m} \times 5^{n}\right)$

Hence, $\frac{17}{30}$ is a non-terminating decimal.