Question

Question 10
The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after

A) One decimal place
B) Two decimal places
C) Three decimal places
D) Four decimal places

Answer 1

The answer is D.
$\frac{14587}{1250}=\frac{14587}{2^1\times 5^4}$
$\begin{array}{cc}2& 1250\\ 5& 625\\ 5& 125\\ 5& 5\\ 5& 1\end{array}$

$=\frac{14587}{10\times 5^3}\times \frac{(2{)}^3}{(2{)}^3}$

$=\frac{14587\times 8}{10\times 1000}$

$=\frac{116696}{10000}=11.6696$
Hence given rational number will terminate after four decimal places.