Question

For a rational number to generate a repeating decimal, what must be true?(1 point) Responses The denominator must be a prime number. The denominator must be a prime number. The numerator must be an odd number. The numerator must be an odd number. The denominator must not evenly divide any power of 10. The denominator must not evenly divide any power of 10. The rational number must not be a mixed number. The rational number must not be a mixed number.

Answer 1

For a rational number to generate a repeating decimal, the correct condition is:

**The denominator must not evenly divide any power of 10.**

This means that if the prime factorization of the denominator, after reducing the fraction to its lowest terms, includes any prime factor other than 2 or 5, then the decimal representation will be repeating.

In other words, if the denominator, when fully factored, has any prime factors that are not 2 or 5, the decimal will repeat. If the denominator is comprised solely of the factors 2 or 5 (or both), the decimal representation will terminate instead.