[tex]0.111...=\dfrac{1}{9};\ 0.222...=\dfrac{2}{9};\ 0.333...=\dfrac{3}{9}=\dfrac{1}{3};\\\\0.444...=\dfrac{4}{9};\ 0.555...=\dfrac{5}{9};\ ...[/tex]
[tex]0.3\overline{2}=0.3222...=0.1+0.2222...=0.1+\dfrac{2}{9}=\dfrac{1}{10}+\dfrac{2}{9}=\dfrac{9}{90}+\dfrac{20}{90}=\dfrac{29}{90}[/tex]
[tex]0.3\overline{2}=\dfrac{9}{20}[/tex]
other method
[tex]x=0.32222...\ \ \ |\cdot10\\\\10x=3.222...\ \ \ \ |\cdot10\\\\100x=32.222...\\\\100x-10x=32.222...-3.222...\\\\90x=29\ \ \ \ |:90\\\\x=\dfrac{29}{90}[/tex]
