[tex] \bf 0.2121\overline{21}\qquad \qquad \qquad x=0.2121\overline{21}\\\\
-------------------------------\\\\
\stackrel{\textit{moving the 21 to the left}}{\stackrel{100\cdot x}{100\cdot 0.2121\overline{21}}}\implies
21.2121\overline{21}\implies
\begin{array}{llll}
21&+&0.2121\overline{21}\\
21&+&x
\end{array}
\\\\\\
therefore\qquad \qquad 100x = 21+x\implies 99x=21
\\\\\\
x=\cfrac{21}{99}\implies x=\stackrel{simplified}{\cfrac{7}{33}} [/tex]
