I was wondering too, but then understood. This is simple school division like column division).
On the example of 21, we putting two 0 to make 100/21 getting 0.0 as a result.
Dividing getting 4 as result (0.04 total) and 16 as remainder.
So we moving one digit right and repeating with 160 getting 0.047 and 13 as a remainder.
Resulting, if we get 1 as a remainder that means that we will repeat the same division process and get same cycled number.
I'm ashamed that I forget the basics...

Can someone explain please what rule inderly the solution?