I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
Imagine the line of 1s is stacked like pages in books on a shelf, but the line of 100s is placed in a row so they're only touching on the sides. You could probably fit a few hundred 1s in the space of one 100. Both lines still have infinite bills in them, but now as you go along, you're seeing a lot more 1s at a time.
That's the thing about infinities, you can squish and stretch them, and they're still infinite.