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Writing Rational Numbers as Decimals

Question

Which of the following will have a non-terminating repeating decimal expansion?
$\frac{15}{800}$
$\frac{29}{630}$
$\frac{11}{2^{2} 5^{3}}$
$\frac{13}{125}$

A

\frac{29}{630}

B

\frac{15}{800}

C

\frac{11}{2^{2} 5^{3}}

D

\frac{13}{125}

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Solution

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By converting the given options to decimal form we get,
$\frac{15}{800} = .01875$

$\frac{29}{630} = .046031746 . . . .$

$\frac{13}{125} = .104$

$\frac{11}{2^{2} 5^{3}} = .022$
By observing the options we see that only one answer is non terminating repeating decimal number.
So, correct answer is option B.

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