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Without actually performing the long divison, find if `(987)/(10500)` will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer

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To determine whether the fraction \( \frac{987}{10500} \) has a terminating or non-terminating (repeating) decimal expansion, we can follow these steps: ### Step 1: Simplify the Fraction First, we need to simplify the fraction \( \frac{987}{10500} \). We can do this by finding the greatest common divisor (GCD) of the numerator and the denominator. 1. **Find the GCD of 987 and 10500**: - The prime factorization of 987 is \( 3 \times 7 \times 47 \). - The prime factorization of 10500 can be calculated as follows: ...
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