>> What is the practical application of computing pi to the umpteenth decimal place?
Still zero
Now, if you remove the term “practical” you could say knowledge in itself is always useful and you never know where it may lead you and it is an end in itself, etc. I do not disagree with this but for now there is no practical use for computing PI to the umpteenth decimal place. Also the same questions may be asked of umpteen billion other numbers which may not be so prominent but are just as scientifically interesting. In many areas of science and finance e is much more prominent than pi.
Now, now…even if I don’t contest your definition of “practical”, Superdude also asked “why bother computing it so far” and (later) “Why is pi so darned mathematically significant”. Both of which deserved answering…
Paying a little more attention to what you said this time, I think we agree. Mankind is no better off for knowing the 3,148,297,483,680th digit of pi.
But, (from what I have read,) a lot of significant knowledge of number theory has come about as a side effect of the quest to calculate the umpteenth digit.