Question

how do you show the group of digits the repeat in a repeating decimal

Answer 1

To show the group of digits that repeat in a repeating decimal, you typically use a bar notation, also known as a vinculum.

For example, let's say you have the repeating decimal \(0.666...\). You would indicate the repeating digit by placing a bar over the digit that repeats:

\[
0.\overline{6}
\]

If a decimal has a more complex repeating sequence, like \(0.123123...\), you would indicate the repeating portion with a bar over the entire repeating sequence:

\[
0.\overline{123}
\]

This notation clearly shows which digits repeat indefinitely. If the decimal has both a non-repeating and a repeating part, such as \(0.1\overline{23}\), where "1" is the non-repeating part and "23" is the repeating part, you would write it as:

\[
0.1\overline{23}
\]

This way of presenting repeating decimals helps to clearly communicate which digits are part of the infinite repetition.