For a rational number to generate a repeating decimal, the decimal representation of the rational number must be non-terminating, meaning it goes on forever. This occurs when the rational number's denominator is not a factor of 10 or its prime factors include other prime factors than 2 and 5.
For a rational number to generate a repeating decimal, the denominator of the rational number must have at least one prime factor that is not a factor of 10. In other words, the prime factorization of the denominator should contain prime factors other than 2 and 5.
