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31 trillion digits is mind blowing precision, so would it matter if it did repeat after that many digit places? Is there some other property of Pi that would make it repeating become significant? Does it really matter at this point whether it repeats or not?

31 trillion digits is mind blowing precision, so would it matter if it did repeat after that many digit places? Is there some other property of Pi that would make it repeating become significant? Does it really matter at this point whether it repeats or not?

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It will never repeat. First, here is a proof that pi is irrational, which means it cannot be expressed as a fraction: https://en.wikipedia.org/wiki/Proof_that_%CF%80_is_irrational

Now take any number, 134 for instance. Divide it by the number of digits in 9's. So in this case it would be 134/999 That will yield a result of 0.134134134...(repeating). Therefore, if pi were to repeat, it could be expressed as a fraction in this manner. Since we know from above that pi is irrational, it cannot be expressed as a fraction. So pi cannot ever repeat.