Given:
[tex]3.1\bar{\text{ 1}}[/tex]Required:
We need to find the equivalent rational number of the given expression.
Explanation:
Recall that In a decimal number, a bar over one or more consecutive digits means that the pattern of digits under the bar repeats without end.
The given number can be written as follows.
[tex]3.1\bar{\text{ 1}}=3.1111111111...[/tex]Conisder the individual options.
1).
[tex]\frac{22}{9}[/tex]Divide 22 by 9.
[tex]\frac{22}{9}=2.44444...=2.4\bar{\text{ 4}}.[/tex][tex]2.4\bar{\text{ 4}}\ne3.1\bar{\text{ 1}}[/tex]2.
[tex]\frac{24}{9}[/tex]Divide 24 by 9.
[tex]\frac{24}{9}=2.666666..=2.6\bar{\text{ 6}}.[/tex][tex]2.6\bar{\text{ 6}}\ne3.1\bar{\text{ 1}}[/tex]3.
[tex]\frac{26}{9}[/tex]Divide 26 by 9.
[tex]\frac{26}{9}=2.88888..=2.8\text{ }\bar{8}.[/tex][tex]2.8\text{ }\bar{8}\ne3.1\text{ }\bar{1}[/tex]4.
