the version number is a tuple, not a decimal, encoded with dots as field separators.
0.10 is an encoding for (0, 10). So 0.10 > 0.9, and 3.7.4a makes perfect sense.
edit: furthermore version number ordering has additional complexity: 3.7.4a < 3.7.4
Dots separate logical numberings, like version, patch, bugfix, etc. So 3.0 goes after 2.0 And 2.0.2 after 2.0.1. And 1.10 after 1.9.
This should be fairly clear given your typical version number takes the form of <integer>.<integer>.<integer> which can't possibly be mistaken for a decimal fraction.
With letters, short hashes or even whole words thrown in.
You can think of a decimal number in the same way (well, leaving out some minor technicalities with numbers requiring infinite expansions here), but you then have to allow only numbers between 0 and 9 (inclusive) in your sequence. Let's leave out positive numbers (because otherwise we'd have to grow sequences in both directions from the decimal point, which is an annoying technicality). Then 0.12345 is simply the sequence (1, 2, 3, 4, 5), which in version notation is 0.1.2.3.4.5. On the other hand, decimal 0.80 is version 0.8.0, not version 0.80.
Really, all in all, version numbers are just decimal expansions, except that we leave out the equivalence relation that says that, for example, 10x10^1 is the same as 1x10^2. So while 0.8.0 and 0.80.0 are distinct version numbers, they collapse to the same value as real numbers (or you might want to collapse 0.80.0 to 8.0 -- it doesn't matter, that's all a matter of taste).
> A version number is a sequence of natural numbers ordered lexicographically.
I need a new rage face for expressing this.
On the other hand, some version numbers can be stored as floats (kind-of, to a point): Knuth's software is versioned using approximations of irrational numbers, the more digits the later the version. TeX's current version is 3.1415926 and METAFONT's is 2.718281. Both can be stored as floats, although the respective and eventual π and e can't be.
In general, I would argue version numbers are sequences of natural numbers ordered lexicographically. That means they're not the same as decimal expansions of real numbers.