Solution

A rational number \( \frac{p}{q} \) has:

• Terminating decimal if \( q \) has only prime factors 2 and/or 5
• Non-terminating repeating decimal if \( q \) has other prime factors

Option (a): \( \frac{39}{24} = \frac{13}{8} \)

Denominator \( 8 = 2^3 \)

✔ Terminating

Option (b): \( \frac{3}{16} \)

Denominator \( 16 = 2^4 \)

✔ Terminating

Option (c): \( \frac{3}{11} \)

Denominator \( 11 \) (not 2 or 5)

✔ Non-terminating repeating

Option (d): \( \frac{137}{25} \)

Denominator \( 25 = 5^2 \)

✔ Terminating

Final Answer

✔ Correct option: (c) \( \frac{3}{11} \)