If is 0.21212121 then
[tex] 0.\underbrace{21212121}_{8}=\dfrac{21212121}{1\underbrace{00000000}_{8}} [/tex]
If is 0.21212121... then
[tex] x=0.21212121...\ \ \ |\cdot100\\100x=21.21212121...\\\\100x-x=21.21212121...-0.21212121...\\\\99x=21\ \ \ |:99\\\\x=\dfrac{21}{99}\\\\x=\dfrac{21:3}{99:3}\\\\x=\dfrac{7}{33}\\\\0.21212121...=\dfrac{7}{33} [/tex]
