Which of the following will have a non-terminating repeating decimal expansion?

\frac{15}{800}

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\frac{29}{630}

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\frac{13}{125}

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

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Solution

The correct option is B $\frac{29}{630}$
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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Question 1 (v)
Without actually performing the long division, state whether $\frac{29}{343}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

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Which of the following will have a non-terminating repeating decimal expansion?

The correct option is B 29630By converting the given options to decimal form we get,15800=.0187529630=.046031746....13125=.104 112253=.022By observing the options we see that only one answer is non terminating repeating decimal number.So, correct answer is option B.