Question

The decimal representation of $\frac{71}{150}$is
(a) a terminating decimal
(b) a non-terminating, repeating decimal
(b) a non-terminating and non-repeating decimal
(d) none of these

Answer 1

(b) a non-terminating, repeating decimal

$\frac{71}{150}=\frac{71}{2\times 3\times 5^2}$
We know that 2, 3 or 5 are not factors of 71.
So, it is in its simplest form.
And, $(2\times 3\times 5^2)$ ≠ $(2^m\times 5^n)$
∴ $\frac{71}{150}=0.47\overline{3}$
Hence, it is a non-terminating, repeating decimal.