How do you show the group of digits it's repeat in a repeating decimal

Answer 1

To show the group of digits that repeat in a repeating decimal, you typically use a line (vinculum) or parentheses. Here are two common methods to indicate the repeating part:

1. Using a Vinculum (Bar): Place a horizontal line over the digits that repeat. For example, for the decimal \(0.333...\), which can be represented as \(0.\overline{3}\), the line over the 3 indicates that it repeats indefinitely.

   Example:

   • \(0.666...\) can be written as \(0.\overline{6}\).

2. Using Parentheses: Enclose the repeating digits in parentheses. For example, the decimal \(0.142857142857...\), which has the repeating part "142857", can be written as \(0.(142857)\).

   Example:

   • \(0.123123123...\) can be written as \(0.(123)\).

These conventions help readers easily identify which part of the decimal repeats. If you have a specific repeating decimal in mind, let me know, and I can help you represent it!