Let
[tex]x=72.111...[/tex]
Multiply x by a power of [tex]10[/tex], one that keeps the decimal part of the number the same:
[tex]10x=721.111..[/tex]
Subtract [tex]x[/tex] from [tex]\\10x[/tex]
[tex]10x-x=721.111-72.111=649[/tex]
The repeating decimals should cancel out
[tex]\\9x=649[/tex]
solve for x
Divide by [tex]9[/tex] both sides
[tex]9x/9=649/9[/tex]
[tex]x=649/9[/tex]
therefore
the answer is
The fraction is [tex]\frac{649}{9}[/tex]
