Question

Has the rational number
$\frac{14587}{1250}$
a terminating or non terminating decimal expansion


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Answer 1

Hey curious!!!

It is a terminating number....Bcz Its denominator has the factors of 5 and 2 ....And any number whose denominatior has factors of 2 or 5 or 2 and 5 both is a terminating no....That's why

Reason: 1250=5×5×5×5×2

Hope this may help you.

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Answer 2

$\huge \tt \overline{hlo \: mate}$

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

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

$= > \frac{116696}{10000}$

$= > 11.6696$

$\huge \tt \overline{terminating}$

hence the decimal will terminate

after 4 decimal places

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