Arbitrary precision is used in applications where arithmetic performance is not a limiting factor, or where precise results or exact integer arithmetic with very large numbers is required. It is also useful for checking the results of fixed-precision calculations. Hence, for APA, we need to look at the accuracy of the results and not at the efficiency.
As for ur query regarding storage of the value of "pi", rational numbers can be stored as a pair of two integers for the numerator and denominator, in a fixed-point format with a fixed denominator, or in a floating-point format as a significand multiplied by an arbitrary exponent.
For further help, you can have a look at these softwares.
Arbitrary-precision software
Arbitrary-precision arithmetic in most computer software is implemented by calling an external library that provides datatypes and subroutines to store numbers with the requested precision and to perform computations.
Stand-alone application software that supports arbitrary precision computations:
