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No, they cannot. Even the concept of "all the digits of pi" is a problem. On the bright side, you don't have to get too many digits in before you have more than enough accuracy for any application you can imagine. Pi may be irrational, but it is reasonable nonetheless. The only digits I memorized to is 3.14159265358979323846264338327950288419716939937510.....that's all a 6th grade math book can give ya.

The number being irrational means that it will go on and on forever. So, because of this is it not possible to know all the digits, because there will always be more to know.

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It is not possible to know all the digits of pi because there are an infinite number of them, in a non-repeating, unpredictable sequence.

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Q: Can all of the digits of pi be fully known?
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