Picture an infinite ticker tape in your mind.

Write

   0.9
 + 0.9
 —————-
   1.8

Now keep extending the 9’s. You have to carry a one, so fix the carry and then add more nines.

Where people keep getting tripped up is thinking you can stop when you get tired, or die, or when the universe ends in heat death. You don’t get to stop. You never get to stop. It’s nines all the way down.

It’s less intuitive, but still relatively straightforward from performing the “long” multiplication. You do need to convince people that the “8 at the end“ is irrelevant, however.