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The decimal expansion of the rational number will $\frac{14587}{1250}$ terminate after:
(A) one decimal place
(B) two decimal places
(C) three decimal places
(D) four decimal places
Given:
Given rational number is $\frac{14587}{1250}$.
To do:
We have to find after how many decimal places the given rational number terminates.
Solution:
If we have a rational number $\frac{p}{q}$, where $p$ and $q$ are co-primes and the prime factorization of $q$ is of the form $2^n.5^m$, where $n$ and $m$ are non-negative integers, then $\frac{p}{q}$ has a terminating expansion.
Now,
$\frac{14587}{1250}=\frac{14587}{2^1\times5^4}$
$=\frac{14587\times2^3}{2^1\times5^4\times2^3}$
$=\frac{14587\times8}{2^4\times5^4}$
$=\frac{116696}{10000}$
$=11.6696$
Hence, the given rational number will terminate after four decimal places.
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