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. :)
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