Question

The decimal expansion of the rational number $\frac{23}{2^3{5}^2}$, will terminate after how many places of decimal?

• A. 1
• B. 3
• C. 4
• D. 5

Answer 1

The correct option is B 3

$\frac{23}{2^3{5}^2}$
= $\frac{23}{2\left(2{)}^2\right(5{)}^2}$
= $\frac{23}{2(2\times 5{)}^2}$
= $\frac{23}{2(10{)}^2}$
= $\frac{11.5}{100}=0.115$

Therefore, the decimal expansion of the rational number $\frac{23}{2^3{5}^2}$
will terminate after three places of decimal.