Question 9
Without actually performing long division, find if $\frac{987}{10500}$ will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.

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Solution

Yes, it has terminating decimal expansion.
We have
$\frac{987}{10500} = \frac{47 \times 21}{500 \times 21} = \frac{47}{500} = \frac{47}{5^{3} {.2}^{2}} \times \frac{2}{2} = \frac{94}{5^{3} \times 2^{3}} = \frac{94}{1000} = 0.094$
Simplified denominator has factor of the form of $2^{m} . 5^{n}$ . So, this is a terminating decimal.

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Question 9 Without actually performing long division, find if 98710500 will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.

Yes, it has terminating decimal expansion. We have 98710500=47×21500×21=47500=4753.22×22=9453×23=941000=0.094 Simplified denominator has factor of the form of 2m.5n. So, this is a terminating decimal.

Question 9
Without actually performing long division, find if $\frac{987}{10500}$ will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.