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.

Answer 1

For a rational number to generate a repeating decimal, the denominator must not evenly divide any power of 10.

In other words, if the rational number is in the form \(\frac{a}{b}\) (where \(a\) is the numerator and \(b\) is the denominator), the decimal will be repeating if \(b\) contains any prime factors other than 2 or 5. If \(b\) is only made up of the primes 2 and 5, the decimal will terminate.

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