Which of the following rational numbers have a non-terminating decimal expansion?
- A
- B
- C
- D
Solution & Step-by-step Explanation
A rational number written in its simplest form has a terminating decimal expansion if the prime factorization of its denominator contains only factors of and/or (i.e., of the form ). If it contains prime factors other than or that cannot be cancelled by the numerator, it has a non-terminating repeating decimal expansion.: Denominator is . (Terminating): Denominator has only and . (Terminating): Denominator contains , which does not divide . (Non-terminating): Contains a factor of in denominator. However, option C represents a purely definitive non-terminating standard configuration. Let's look closer at C: the factor clearly stays.