## Introductory Algebra for College Students (7th Edition)

$0.\overline{81}=0.81818181...$
If we can write a fraction so that its denominator is one of 10,100, 1000,..., we can easily write it as a decimal number The denominator is $11$, and it is not a factor of any of the numbers mentioned. In that case we perform division (numerator) (denominator) $9\div 11 =$ $9.0000000\div 11=$ (after long division) $=0.8181818181...$, which is a periodic number with a group of two repeating digits, which we write as $=0.\overline{81}$