Question

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.

\[\frac{987}{10500}\]

Answer 1

The given number is \[\frac{987}{10500}\].

\[\frac{987}{10500} = \frac{987 \div 21}{10500 \div 21} = \frac{47}{500}\]

Now, 500 = 2² × 5³
The denominator can be written in the form of 2^m × 5ⁿ.
So, the given number has a terminating decimal expansion.

\[\frac{987}{10500} = \frac{47}{500} = \frac{47}{5^3 \times 2^2} \times \frac{2}{2} = \frac{94}{5^3 \times 2^3} = \frac{94}{1000} = 0 . 094\]