To solve the problem of identifying which option correctly uses bar notation to represent the repeating decimal for [tex]\(\overline{11}\)[/tex], let's recall what bar notation for repeating decimals means. Bar notation puts a line (or "bar") over the digits that repeat indefinitely in the decimal representation.
First, consider the given choices:
1. [tex]\(0.5\overline{4}\)[/tex]
2. [tex]\(0.54\overline{54}\)[/tex]
3. [tex]\(0.\overline{54}\)[/tex]
4. [tex]\(0.\overline{545}\)[/tex]
To determine the correct option:
1. [tex]\(0.5\overline{4}\)[/tex]: This notation means 0.544444..., where only the digit 4 repeats.
2. [tex]\(0.54\overline{54}\)[/tex]: This notation means 0.5454545454..., where the sequence 54 repeats.
3. [tex]\(0.\overline{54}\)[/tex]: This notation means 0.54545454..., where the sequence 54 repeats.
4. [tex]\(0.\overline{545}\)[/tex]: This notation means 0.545454545..., where the sequence 545 repeats.
The correct notation to represent the repeating decimal "54" is [tex]\(0.\overline{54}\)[/tex]. This option (3) indicates that "54" repeats indefinitely after the decimal point.
Therefore, the answer to the question is:
[tex]\[
\boxed{3}
\][/tex]
