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

The denominator must not evenly divide any power of 10.

Rational numbers in the form of fractions will produce a repeating decimal if, when expressed in lowest terms, the denominator has prime factors other than 2 and 5. If the denominator consists only of the prime factors 2 and 5, then the decimal representation will terminate.

Question

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

The denominator must not evenly divide any power of 10.

Rational numbers in the form of fractions will produce a repeating decimal if, when expressed in lowest terms, the denominator has prime factors other than 2 and 5. If the denominator consists only of the prime factors 2 and 5, then the decimal representation will terminate.

GPT-4o mini · Answer

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

The denominator must not evenly divide any power of 10.

Rational numbers in the form of fractions will produce a repeating decimal if, when expressed in lowest terms, the denominator has prime factors other than 2 and 5. If the denominator consists only of the prime factors 2 and 5, then the decimal representation will terminate.