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प्रश्न
Without actually performing the long division, state whether state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion.
उत्तर
The given number is \[\frac{987}{10500}\].
Now, 500 = 22 × 53
The denominator can be written in the form of 2m × 5n.
So, the given number has a terminating decimal expansion.
\[\frac{987}{10500} = \frac{47}{500} = \frac{47}{5^3 \times 2^2} \times \frac{2}{2} = \frac{94}{5^3 \times 2^3} = \frac{94}{1000} = 0 . 094\]
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