2016 · Q13
Which one of the following rational numbers has non-terminating and repeating decimal expansion ?
Elementary MathematicsNumber System
- A15/1000
- B23/8
- C35/50
- D17/6
Explanation
A rational in lowest terms has a terminating decimal iff its denominator's prime factors are only 2 and 5. That holds for 15/1000, 23/8 and 35/50, but 17/6 has denominator 6 = 2×3. Hence only 17/6 repeats non-terminatingly (option D).