Question

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

Answer 1

For a rational number to generate a repeating decimal, the denominator must not evenly divide any power of 10. This means that the denominator can have prime factors other than 2 and 5 for the decimal representation to be repeating. If the denominator is comprised solely of the prime factors 2 and/or 5, the decimal will terminate instead.

So, the correct response is: The denominator must not evenly divide any power of 10.