Without actually performing the long division find if 987-10500 will have terminating or nonterminating repeating decimal expansion- - Maths Q-A

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Standard IX

Mathematics

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Question

Without actually performing the long division, find if $\frac{987}{10500}$ will have terminating or nonterminating repeating decimal expansion. Give a reason for your answer.

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Solution

Find if $\frac{987}{10500}$ will have terminating or nonterminating repeating decimal expansion.
A fraction is a terminating decimal if the denominator can be expressed in the form of $2^{m} \times 5^{n}$ .
Now,
$\frac{987}{10500} = \frac{3 \times 7 \times 47}{2 \times 2 \times 3 \times 5 \times 5 \times 5 \times 7} = \frac{47}{2 \times 2 \times 5 \times 5 \times 5} = \frac{47}{2^{2} \times 5^{3}}$
As, the factors of denominator are in the form of $2^{m} \times 5^{n}$ .
So, $\frac{987}{10500}$ will have terminating repeating decimal expansion.
Thus, $\frac{987}{10500}$ will have terminating repeating decimal expansion.

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Without actually performing the long division, find if 98710500 will have terminating or nonterminating repeating decimal expansion. Give a reason for your answer.

Without actually performing the long division, find if $\frac{987}{10500}$ will have terminating or nonterminating repeating decimal expansion. Give a reason for your answer.