If you divide 1 by 7, you'll of course have a repeating decimal sequence of `142857`. This of course repeats forever. Are there any scenarios where a quotient seems to repeat forever, but then changes at some point? Is this even possible? I'm not a mathematician (obviously), but rather a programmer. The question came up when I was thinking of a programmatic way to determine whether a division result is repeating.


Example (not real of course):



```
113548718971135487189711354871897113548718974898711

```

P.S. I can't even find an appropriate tag for this question, so feel free to edit my tags.



Is it possible for a large repeating sequence to appear in a non-repeating division quotient?
If you want to check if the result of the division is repeating you can make use of this (from 
<http://www.mathlesstraveled.com/?p=134>):



> the decimal representation of any rational number will either terminate, or eventually become periodic. (As a bonus challenge, can you figure out how to tell the difference between rational numbers whose decimal expansion terminates, and those whose expansion repeats?) Note that we also know something else: since there are only (q-1) possible non-zero remainders when dividing by q, the repeating portion of the decimal expansion of a rational number with a denominator of q can be at most (q-1) digits long. It could be shorter, but it can’t be any longer. You can also look at this in reverse; for example, if you see a periodic decimal whose repeating portion is ten digits long, you know that the rational number it represents must have a denominator of at least 11.


So in your example I think you would only need to check up to the 7th digit and for sleepless's example, you would only need to check up the 13th digit.


I'm also a programmer and not a mathematician so I probably have this all wrong :)


