What is 0.21212121 ... as a fraction

If we make the number equal to x ...

0.21212121 ... = x

multiply each side by 100

21.212121 ... = 100x

remember that x is 0.21212121? we can subtract that now from 21.21212121, as well as x from 100.

21.212121 ... - 0.212121 ... = 100x - x

we are left with 21 = 99x

21 = 99x

simplify ...

7 = 33x

and divide!

7/33 = x

Your answer is: 0.2121212121 ... = 7/33

If numbers repeat, it's problby divided by 9 or some multipule of 9

if 2 numbers repeat, it's probbalby divided by 99

like 0. abababababab=ab/99

so

0.21212121

21 repeats

so it is 21/99 or 7/33