First, that's exactly the right answer.
To quibble a little bit, computers don't manipulate numbers in the abstract, they store them in binary. (You can just say "internal representation" if you want to pretend that anyone is using a non-binary computer.)
Now I'm just getting silly. You could, technically, write code to multiply numbers by directly working on their (decimal or hex) string representations, using the grade school long-form method. It would be a million times slower, because you're emulating something the computer can do in one instruction, but you could do it.
So, once again, listen to Laurent. Put the numbers in a form the computer can work with easily, let it do its magic, then convert them back to the form you want to look at.