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

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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 is terminating decimal expansion. Simplified denominator has factor in the form of 2m.5n. So, this is terminating decimal. Now, 98710500=47500=4753.23×22=9453×23=941000=0.094

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.

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