Choose the correct answer from the given four options in the foll… - Vidyadip

MCQ

Choose the correct answer from the given four options in the following questions:
The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after:

A
One decimal place.
B
Two decimal places.
C
Three decimal places.
✓
Four decimal places.

✓

Answer

Correct option: D.

Four decimal places.

Rational number $=\frac{14587}{1250}=\frac{14587}{2^{1}\times5^{4}}$
$=\frac{14587}{10\times5^{3}}=\frac{(2)^{3}}{(2)^{3}}$
$=\frac{14587\times8}{10\times1000}$
$=\frac{1166969}{10000}=11.6696$
Hence, given rational number will terminate after four decimal places.
$\begin{array}{c|c} 2 & 1250 \\ \hline 5 & 625 \\ \hline 5 & 125 \\ \hline 5 & 25 \\ \hline 5 & 5 \\ \hline & 1 \end{array}$

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