Total math novice here. I'm wondering if (as I think should be the case) there is no maximum length of a repeating decimal period, for example:
- 0.33333... (period 1) - 0.252525... (period 2) - 0.142857142857... (period 6) - etc.
The reason I am curious about this is that I have learned that the decimal expansions of irrational numbers don't terminate or repeat. But if there is no upper limit to the period that a repeating decimal can have, then where is the difference between the two? I am guessing that although the repeting pattern can grow without bound it is always finite (I think?) whereas with an irrational number the pattern never restarts again after a finite period. But it still makes my head hurt :-) so I am wondering if there are any explanations for it that I might be able to understand as a non-practitioner.
Thanks for any help!