Evaluate the infinite geometric series 0.79 + 0.079 + 0.0079 + 0.00079 + 0.000079 + \dotsb. Express your answer as a fraction.

$$\small{\text{ The fraction is
$\dfrac{79}{90}
$}}$$

$$\small{
\text{sum $ \ s = \underbrace{(7.9*10^{-1})}_{=a} + (7.9* 10^{-1} ) * 10^{-1} + (7.9* 10^{-1} ) * 10^{-2} + (7.9* 10^{-1} ) * 10^{-3} + \dots + (7.9* 10^{-1} ) * 10^{-(n-1)}
$
}}$\\\\\\$
\small{\text{
$
r = \dfrac{ (7.9* 10^{-1} ) * 10^{-1} }{ (7.9* 10^{-1} )} = 10^{-1}
$
}}$\\\\$
\small{\text{
$
s = \dfrac{ a }{ 1-r } = \dfrac{(7.9* 10^{-1} ) }{1-10^{-1} }
$
}}$\\\\$
\small{\text{
$
s = \dfrac{(7.9* 10^{-1} ) }{1- 10^{-1} } * \dfrac{ 10^{1}}{10^{1} }
$
}}$\\\\$
\small{\text{
$
s = \dfrac{ 7.9 } { 10^{1} -1} = \dfrac{7.9}{9}
$
}}$\\\\$
\small{\text{
$
s = \dfrac{7.9}{9} = 0.87777777777777777777777777\overline{7} = 0.8\overline{7}
$
}}$$

sorry, but what is the fraction for this?

thank you so much Heureka!