Question

The decimal expansion of the rational number `14587/1250` will terminate after ______.

Options

• One decimal place

• Two decimal places

• Three decimal places

• Four decimal places

Answer 1

The decimal expansion of the rational number `14587/1250` will terminate after four decimal places.

Explanation:

`14587/1250 = 14587/(2^1 xx 5^4)`

= `14587/(10 xx 5^3) xx (2)^3/(2)^3`

= `(14587 xx 8)/(10 xx 1000)`

= `116696/10000`

= 11.6696

Hence, given rational number will terminate after four decimal places.