Are you concerned about accuracy or precision? In general, accuracy is "how close to the correct value is my answer", while precision is "how many significant digits does my answer contain."
in reply to machine accuracy
What you are describing is precision - and as someone else mentioned, bignum could be your friend. However, once you start manipulating high precision values, you need to make sure your numerical methods do not reduce your accuracy. In the dim, dark past, I did an honours-level university applied math subject that dealt with how to structure calculations so that numerical rounding errors did not accumulate and destroy your accuracy. Sadly, I have forgotten much of it!