Decimal Points and Binary Points

How can you take 100.1 (binary) and get 4.5 (decimal)

I understand that:

100(binary) = 4.0(dec) because that is the same as saying there are no ones, no twos, and one four.

I also understand 1101 to mean 13 because there it is 1 + (0 * 2) + (1 * 4) + (1 * 8).

I don't understand how 100.1(bin) can equal 4.5(dec). I would have thought it to mean 4.1

Can you have a binary number be something like 2021 which in decimal would be (1 * 1) + (2*2) + (0 * 4) + (2 * 8). It is still in binary powers, it is just saying how many of each power exists.

EDIT

and btw this is from a book, in case u cared!