Question

Which of the following has a terminating decimal expansion?

• A. \( \frac{11}{700} \)
• B. \( \frac{91}{2100} \)
• C. \( \frac{343}{2^3 \times 5^3 \times 7^3} \)
• D. \( \frac{15}{2^5 \times 3^2} \)

Hint:

A fraction \( \frac{p}{q} \) has a terminating decimal expansion if \( q \) contains only 2 and/or 5 as prime factors.

Answer 1

The Correct Option is C

A fraction has a terminating decimal expansion if its denominator contains only the prime factors 2 and 5.
- \( \frac{11}{700} \) has 7 in the denominator → Non-terminating.
- \( \frac{91}{2100} \) has 7 in the denominator → Non-terminating.
- \( \frac{343}{2^3 \times 5^3 \times 7^3} \) has only 2, 5, and 7 in the denominator → Terminating.
- \( \frac{15}{2^5 \times 3^2} \) has 3 in the denominator → Non-terminating.
Thus, the correct answer is \( \frac{343}{2^3 \times 5^3 \times 7^3} \), which has a terminating decimal expansion.