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

In more detail, a rational number expressed in the form \(\frac{p}{q}\) (where \(p\) is the numerator and \(q\) is the denominator) will generate a terminating decimal if the denominator \(q\) (when in its simplest form) has no prime factors other than 2 and 5. If \(q\) has any other prime factors, the decimal representation will repeat.

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

Question

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

In more detail, a rational number expressed in the form \(\frac{p}{q}\) (where \(p\) is the numerator and \(q\) is the denominator) will generate a terminating decimal if the denominator \(q\) (when in its simplest form) has no prime factors other than 2 and 5. If \(q\) has any other prime factors, the decimal representation will repeat.

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

GPT-4o mini · Answer

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

In more detail, a rational number expressed in the form \(\frac{p}{q}\) (where \(p\) is the numerator and \(q\) is the denominator) will generate a terminating decimal if the denominator \(q\) (when in its simplest form) has no prime factors other than 2 and 5. If \(q\) has any other prime factors, the decimal representation will repeat.

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