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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Updated on: 10-Oct-2022

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