Question on recurring decimal digits

In my discrete maths class, I have come across an interesting phenomenon for which I can't find an explanation!

If we divide $1$ by $13$ we obtain $0.07692307\dots $

If we divide $3$ by $13$ we obtain $0.23076923\dots $

If we divide $4$ by $13$ we obtain $0.30769230\dots $

As you can see, the digits are recurring in the same order but starting at a different point in the sequence.

Can someone explain this to me? What exactly is happening here?

In my discrete maths class, I have come across an interesting phenomenon for which I can't find an explanation!

If we divide $1$ by $13$ we obtain $0.07692307\dots $

If we divide $3$ by $13$ we obtain $0.23076923\dots $

If we divide $4$ by $13$ we obtain $0.30769230\dots $

As you can see, the digits are recurring in the same order but starting at a different point in the sequence.

Can someone explain this to me? What exactly is happening here?