Step-by-step explanation:
If 21 is not repeating, then it's easy.
[tex]0.\underbrace{21212121}_8=\dfrac{21212121}{1\underbrace{00000000}_8}[/tex]
If If 21 is repeating, then the solution is:
[tex]x=0.21212121...\qquad\text{multiply both sides by 100}\\\\100x=21.212121...\\\\100x-x=21.212121...-0.212121...\\\\99x=21\qquad\text{divide both sides by 99}\\\\x=\dfrac{21}{99}\\\\x=\dfrac{21:3}{99:3}\\\\x=\dfrac{7}{33}[/tex]
