300 significant digits is a lot. System.Double represents up to about 15 digits, according to the documentation.
There's no arbitrary-precision float class in the .NET framework that I know of. If you know how many decimal places your numbers will have, and aren't performing a lot of math operations on them, you could look at using System.Numerics.BigInteger. This will store an arbitrary-length integer, and you could then apply a scaling factor whenever you output the number.
If 300 was a typo, and you only need 30 significant digits, that's within the range of quad-precision. That's not built into the framework, but I see a quad precision library on CodePlex, and there are probably others.
Otherwise, you'll need to find or implement your own arbitrary-precision library to handle these values.