So far it's been calculated to well over a trillion decimal places ! The final answer will never be known - since the value of Pi is a never-ending number that (up to now) doesn't exhibit any repetitive sequence of digits. Theoretically, someone could calculate the number for the rest of their lives and never reach a final solution !
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A Japanese psychiatrist memorized 83,431 digits of pi. This man is Akira Haraguchi.
It's been proven that pi is an irrational number. In other words, it can't bewritten with a finite number of digits, and there is no 'last digit'.
3.14159265358979323846264338327950288419716939937510582097494459230781640628620 8998628034825342117067982148086513282306647093844609550582231725359408128481117 4502841027019385211055596446229489549303819644288109756659334461284756482337867 8316527120190914564856692346034861045432664821339360726024914127372458700660631 5588174881520920962829254091715364367892590360011330530548820466521384146951941 511609.. pi is not discovered...it is calculated. It is an unending number and millions of digits have been calculated.
Answer: No. Pi is irrational; we could never find the last digit, because the digits go on forever. Also, being irrational means that the digits don't repeat periodically.