Question

The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after :

(a) one decimal places (b) two decimal places
(c) three decimal place (d) four decimal places

Answer 1

Consider the rational number $\frac{14587}{1250}$.

Now, 1250 = 5⁴ × 2

The denominator can be written in the form of 2^m × 5ⁿ.

So, the given number has a terminating decimal expansion.

$\frac{14587}{1250}=\frac{14587}{5^4\times 2^1}=\frac{14587\times 8}{5^4\times 2^4}=\frac{116696}{10000}=11.6696$

The given rational number will terminate after four decimal places.

Hence, the correct answer is option D.