Pi Approximation Day

[Gerson W. Barbosa]

Thank you all for your comments!

Yes, I am having an approximately good day (I wish the numbers on the callendar weren't a reminder I am getting older -- 58 and counting :-)

Now, time for a little riddle.

The following appears to be a pretty bad approximation. It really is, depending on how we look at it. However, when I change only one digit or, equivalently, when I remove one of its parts, it returns a perfect 10-digit result on my HP-41C, which I am using to evaluate it. BTW, I have used the HP-41C for this one because of its 10-digit display and a seldom used useful built-in function which most of my Voyagers lack. Too many tips, but it doesn't matter :-)

Have fun!

\(\frac{\frac{26}{7}-\frac{6}{11211}}{\left (\frac{4141}{3313}\right ) ^{\frac{3}{4}}}\)

Edited to include a pair of parentheses in order to avoid ambiguity