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

Question

Responses

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.

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.

Answer 1

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

The denominator must not evenly divide any power of 10.

This means that if a rational number is expressed in its simplest form as \( \frac{p}{q} \), where \( p \) is the numerator and \( q \) is the denominator, then \( q \) must contain prime factors other than 2 and 5 for the decimal representation to be repeating. If \( q \) only contains the prime factors 2 and 5, the decimal representation will terminate.