sequences and series - Is there any explanation for the repetitions after decimal point on divisions like 24/7

I was trying to divide 24 by 7 using a pen and a paper.

After I had no more space on my checkerboard paper, I decided to put it on a calculator.

The calculator returned 3.428571428571429 and I noticed it rounded up the last ( an 8 became 9) digit so the algorithm could stop.

But in my accounts the number is 3.428571428571428571428571428571...

So I calculated it on a high precision calculator, and I noticed the pattern 857142 will repeat indefinitely.

I already knew this can happen when you do such divisions, now I always wondered myself and asked my teachers but never got an answer to why the numbers repeat themselves. I mean, I could have a whole sort of random numbers and that'd be ok, I just wonder why they have this pattern.

Is there any article or study on that so I can read it?

Answer

The answer is: long division.

Do the long division and you'll see 'an explanation for the repetitions after decimal point' yourself. :)