Decimals that repeat or continue without repeating are categorized into two types: repeating decimals and non-repeating, non-terminating decimals.
1. **Repeating decimals:** These are decimals where a pattern repeats indefinitely. To represent repeating decimals, a bar is placed over the repeating part. For example, \(0.666\ldots\) is represented as \(0.\overline{6}\).
2. **Non-repeating, non-terminating decimals:** These decimals neither repeat nor terminate. They go on indefinitely without forming a clear pattern. Examples include \(\pi\) (pi) or \(\sqrt{2}\).
When working with repeating decimals, you often use the bar notation to represent the repeating part. When dealing with non-repeating, non-terminating decimals, you may use mathematical symbols or expressions to represent them, as they cannot be precisely expressed as a finite decimal or fraction.