Binary decimals?

So I love a good xkcd as much as the next nerd, but this one got me thinking a little too much:

To wit, what is the probability? I mean, part of that is the assessment of the girl's GI (Geek Index), but then also how does one break up the "number line" between 1 and 10 in binary? I mean, in decimal, you can have 1.0, 1.1, 1.2 ... 1.9, 2.0, which one can also write as 1 + a fraction: 1 + 0/10, 1 + 1/10 .. 1 + 10/10.

Those same fractions, in binary, become 1 + 0/10, 1 + 1/10, and 1 + 10/10 = 1 + 1 = 10, so it seems as though there is one fraction "halfway" between 1 and 10, with the option for infinite continued bisection. But is that a notational trick? I really have no idea what "1.5" in binary means.

P.S. I'm sure the internet has an answer, but at this point I don't feel like looking. Or rather, it's kinda fun remaining ignorant and spending a couple minutes pretending Google doesn't exist.