Question:
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
Solution:
(d) Rational number $=\frac{14587}{1250}=\frac{14587}{2^{1} \times 5^{4}}$
$=\frac{14587}{10 \times 5^{3}} \times \frac{(2)^{3}}{(2)^{3}}$
$=\frac{14587 \times 8}{10 \times 1000}$
$=\frac{116696}{10000}=11.6696$
Hence, given rational number will terminate after four decimal places.
