A rational number, by definition, is a number that can be expressed as the quotient or fraction \(\frac{p}{q}\), where \(p\) is an integer and \(q\) is a non-zero integer. All rational numbers can be expressed as either terminating or repeating decimals.
A decimal is considered a repeating decimal if the decimal representation of the number has a portion that repeats indefinitely after some initial digits.
For example:
- The rational number \(\frac{1}{3}\) can be expressed as \(0.333...\), which is a repeating decimal.
- The rational number \(\frac{1}{6}\) can be expressed as \(0.1666...\), which is also a repeating decimal.
- The rational number \(\frac{1}{4}\) can be expressed as \(0.25\), which is a terminating decimal.
If you provide a specific list of rational numbers, I can help identify which ones can be expressed as repeating decimals. In general, any rational number that is not a terminating decimal will be a repeating decimal.
Please provide the list of numbers you're considering!