I remember a conversation I had with my daughter in the car when she was starting out with algebra...

Me: Is 9.999... the same as 10, or is it just really close to 10?

Kid: Really close. It never gets all the way there.

Me: Well then how close? What do you get when you subtract 9.999... from 10?

Kid: (pause) An infinite number of zeroes. . .and then a one. . .wait, you can't do that.

Me: Right. You just have an infinite number of zeroes. Which is zero.

Kid: (pause) Oh, that's mind-blowing.