It is an irrational number. All Irrational Numbers have infinitely long non-recurring representations in the decimal system. Using the binary, octal, hexadecimal or any other rational base will not make a difference. The representation will remain infinitely long and non-recurring.
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And what use can you make of so many digits? 10-15 digits are more than enough for any practical calculation. Anyway, search Google for "digits of pi", and you'll get several places where pi is listed to many digits.
pi is an irrational number so there are no sustained patterns in the digits of pi.
There is 5 trillion digits of pi.
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A Japanese psychiatrist memorized 83,431 digits of pi. This man is Akira Haraguchi.