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

Responses

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

The rational number must not be a mixed number.
The rational number must not be a mixed number. - no response given

The denominator must be a prime number.
The denominator must be a prime number. - no response given

The denominator must not evenly divide any power of 10.

1 answer

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 for a fraction in its simplest form, if the only prime factors of the denominator are 2 and/or 5, it will result in a terminating decimal. However, if the denominator has prime factors other than 2 and 5 (for example, 3 or 7), then the decimal representation will be repeating.