Question

The decimal expansion of the rational number $\frac{14587}{1250}$ is terminating after ___ .

• A. five decimal places
• B. four decimal places
• C. three decimal places
• D. two decimal places

Answer 1

The correct option is B four decimal places

Rational number = $\frac{14587}{1250}$ = $\frac{14587}{2^1\times 5^4}$

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

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

= $\frac{14587\times 8}{10\times {10}^3}$

= $\frac{116696}{{10}^4}$

= $\frac{116696}{10000}$

= $11.6696$
Hence, the given rational number will terminate after four decimal places.