besides bignum, you can also try some multiprecision package. This implies in general having a C library and a Perl module to interface with it. A example is Math::GMP or Math::Pari. Can be better to store everything first as strings and deal with separtely with exponents.

if you want to try Math::Pari, on some systems there is a bug which prevents the build to fetch correctly the Pari lib. If you fetch it yourself and untar it in the module install dir everything should be fine