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- It's commonly known the decimal expansion of an irrational number never repeats or terminates. The word 'never' made me think what about the case for rational numbers. Are there rational numbers with infinite decimal expansions that repeats just once, or any finite number of times?
It seems like there is no number whose infinite decimal expansion has a finite number of repeated segments, since if the repeated segment is finite in length, it must be repeated an infinite number of times for the repetition to continue indefinitely. And if the repeated sequence is infinite in length, then there cannot be a repeat since the segment itself goes on indefinitely.