I don't get Golomb / Rice coding: It does make more bits of the input, or does it?

Or, maybe, what I don't get is unary coding:

In Golomb, or Rice, coding, you split a number N into two parts by dividing it by another number M and then code the integer result of that division in unary and the remainder in binary.

In the Wikipedia example, they use 42 as N and 10 as M, so we end up with a quotient q of 4 (in unary: 1110) and a remainder r of 2 (in binary 010), so that the resulting message is 1110,010, or 8 bits (the comma can be skipped). The simple binary representation of 42 is 101010, or 6 bits.

To me, this seems due to the unary representation of q which always has to be more bits than binary.

Clearly, I'm missing some important point here. What is it?