For example, a value [of pi] truncated to 11 decimal places is accurate enough to calculate the circumference of a circle the size of the earth with a precision of a millimeter, and one truncated to 39 decimal places is sufficient to compute the circumference of any circle that fits in the observable universe to a precision comparable to the size of a hydrogen atom.
A double precision floating point number truncates at around sixteen decimal places- (and this is a very naive storage method for numbers like pi and e, the significand could and should be longer than the IEEE standard). Please, I would like to hear about your real world application that requires pi to a greater accuracy than this, Sir.