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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
Solution
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.
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