Question

The decimal expansion of the rational number $\frac{33}{2^2\times 5}$ will terminate after
(a) one decimal place (b) Two decimal places
(c) three decimal places (d) more than 3 decimal places

Answer 1

Consider the rational number$\frac{33}{2^2\times 5}$.
Denominator of the above rational number is of the form $2^m\times 2^n$, so the rational number has terminating decimal expansion.
$\frac{33}{2^2\times 5}=\frac{33\times 5}{2^2\times 5^2}=\frac{165}{100}=1.65$
So, the decimal expansion of the given rational number terminates after two decimal places.

Hence, the correct answer is option B.