I'd like to draw a better comparison in order to elucidate the incredible accuracy of 100 digits of pi (which are necessary for admission to our club):
Imagine a sphere with a radius from earth to sirius (8.7 lightyears). Fill it up with bacilli such that each cubic millimetre contains 1 trillion ( = 1 000 000 000 000) bacilli. Now string them all to a row so that the intervall between the first and the second bacillus amounts to the distance earth - sirius, the same with the second and third bacillus, the third and fourth, and so on. Take the distance from the first to the last bacillus as the radius of a sphere. Calculating the circuit of that sphere by using 100 digits of pi results in an error smaller than a ten millionth of a millimetre!!!
So why do we need 51 billion digits of pi and more?
Because pi is most beautifull! Calculating more digits of pi increases the amount of beauty in the world!