^^^ Good advice.
Last year before I did my first centuries, I did several metric centuries (62 miles). Although you do increase your fitness by doing these longer rides, the really important part is that you also boost your confidence so that you know you can make it.
Centuries (unless you are going for speed) are less about fitness, and more about eating/drinking and staying comfortable on the bike. You won't be able to store enough energy even with a big dinner to last beyond a couple hours, so you need to "refuel" on the run. And any little pain gets magnified. I've never really been "tired" after any of the three centuries I've done, but my butt was definitely a little sore!
Another thing to keep in mind is that a 100 mile ride is just 2 and half of your 40 mile rides, and you can take whatever break you want to between segments.