If you have a number _x_ of the form:

    a.bc

Where `a` is the integer part, `b` is the non-repeating fractional part, and `c` is the repeating fractional part, then the resulting fraction has value:

    a.b + c / ((10^num_digits(c) - 1) * 10^num_digits(b))

So for 0.333333... we have:

    a = 0
    b = 0
    c = 3

Giving:

    0.0 + 3 / ((10^1 - 1) * 10^0)
    1 / 3

The more complex .20151515151515... we have:

    a = 0
    b = 20
    c = 15

Giving:

    0.20 + 15 / ((10^2 - 1) * 10^2)
    133 / 660