\[0,888\ldots = 0,8 + 0,08 + ...\]
\[q = 0,1;\]
\[S = \frac{0,8}{1 - 0,1} = \frac{0,8}{0,9} = \frac{8}{9};\]
\[0,888\ldots = \frac{8}{9}.\]