For a rational number to generate a repeating decimal, what must be true?(1 point)

Question

Responses

The numerator must be an odd number.
The numerator must be an odd number.

The denominator must be a prime number.
The denominator must be a prime 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.

This means that if the denominator (in its simplest form) has prime factors other than 2 or 5, the decimal representation will be repeating. If the denominator consists only of the prime factors 2 and/or 5, then the decimal representation will terminate.