Question

What is 0.21212121.... as a fraction

Answer 1

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

Answer 2

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