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

Answer 1

The correct option is D four decimal places

It can be written as:

$\frac{14587}{1250}=\frac{14587}{2^1\times 5^4}$ (Since $14587$ and $1250$ are co-primes).

Since, the denominator is in $2^n\times 5^m$ form, where $n=1$ and $m=4$, the given rational number have a terminating decimal expansion.

Also,

$\frac{14587}{1250}=\frac{14587}{2^1\times 5^4}\times \frac{2^3}{2^3}$

$=\frac{14587\times 8}{2^4\times 5^4}$

$=\frac{116696}{(2\times 5{)}^4}$

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

$=\frac{116696}{10000}$ $=11.6696$.

Therefore, the given rational number terminates after four decimal places.

Thus, option $D$ is correct.