[tex]\dfrac{82}{9}=\dfrac{81+1}{9}=\dfrac{81}{9}+\dfrac{1}{9}\\\\=9\frac{1}{9}[/tex]
If you're doing this by long division, you recognize that the largest multiple of 9 that is less than 82 is 81 = 9×9. When you subtract 81 from 82, you have a remainder of 1. That is, the quotient is 9 + 1/9.
If you keep doing the decimal division, you find the remainder continues to be 1, so the decimal repeats indefinitely: 9.11111111....
