What I was aiming at is, that Perl makes no distinction between the base of numbers. You may specify a number in hexadecimal notation, that is, starting with 0x, or as a plain integer, that is, in decimal notation, or in octal notation, starting with a leading zero. Internally, Perl will treat all these as numbers, because they get converted to the Perl-internal representation for numbers.
If you have a string and you want to perform arithmetic operations on it, the easiest way to do that is if the string looks_like_number, that is, is in decimal notation (at least for this discussion). Otherwise, you have to convert from the notation you have to the decimal notation. For example, the functions hex and oct do that.
But maybe, we can just leave the plane of metaphysical discussions of the representation of numbers, and the numbers themselves (and whether numbers exist without representation) and you tell us what problem you're trying to solve?