+26376 Find 
$$\left
\begin{array}{rcl}
10 \times 0.\overline{9} &=& 9.\overline{9} \\
1 \times 0.\overline{9} &=& 0.\overline{9}
\end{array} \right\} -
\\
\hline$$
$$\begin{array}{rcl}
(10-1)\times 0.\overline{9} &=& 9.\overline{9} - 0.\overline{9} \\
9 \times 0.\overline{9} &=& 9 \\
9 \times 0.\overline{9} &=& 9 \qquad | \qquad : 9 \\
0.\overline{9} &=& \dfrac{9}{9} \\
0.\overline{9} &=& 1 \\
\end{array}$$
= 1 - 1 = 0
+128731 Note that........
(1.00000....) - (.9999......) = .(00000).....1 = .01 where the "bar" is over the "0'
{sorry.....I dont know how to insert the bar !!!}
+118613 $$\\0.\bar3=\frac{1}{3}\\\\
3*0.\bar3=3*\frac{1}{3}\\\\
therefore\\
0.\bar9=1\\\\\\
1-0.\bar9 = 1-1 = 0$$
+26376 Find
$$\left
\begin{array}{rcl}
10 \times 0.\overline{9} &=& 9.\overline{9} \\
1 \times 0.\overline{9} &=& 0.\overline{9}
\end{array} \right\} -
\\
\hline$$
$$\begin{array}{rcl}
(10-1)\times 0.\overline{9} &=& 9.\overline{9} - 0.\overline{9} \\
9 \times 0.\overline{9} &=& 9 \\
9 \times 0.\overline{9} &=& 9 \qquad | \qquad : 9 \\
0.\overline{9} &=& \dfrac{9}{9} \\
0.\overline{9} &=& 1 \\
\end{array}$$
= 1 - 1 = 0
