Write in the form of a fraction the number

$$
x=0,512341234123412341234123412341234 \ldots
$$
On a

$$
10 x=5,123412341234123412341234 \ldots
$$

and

$$
100000 x=51234,1234123412341234123412341234 \ldots
$$

so $99990 x=51229$ and finally $x=\frac{51229}{99990}$. We can generalize this method to any number that has a repeating decimal expansion.