For example (and I don't know if this is actually true), I once read that knowing π to nine decimal places allows you to calculate the circumference of the observable universe to the precision of the width of a hydrogen atom. It's hard to imagine needing much more precision than that.
It's not true. If pi is truncated to 9 decimal places then the magnitude of the error is approximately 5×10
-10.
Now imagine a circle of radius 1km = 10
6mm. Using the approximate value of pi the error in the calculation of the area will be of the magnitude
5×10-10×1012mm2=500mm2.
I heard about this yesterday. That's cool from a theoretical standpoint. But the part of my engineer personality that likes practical things is wondering what it is we actually do with a 17 million digit number.
I was listening to the tail end of an interview with the guy who was in charge of the project and he was asked the same question. He agreed that the number itself is of no use at the moment but what is useful is the method by which the number was found
ie spreading a huge computational problem over lots of small computers.