if you ever go and calculate it by hand or calculator you'd find that 22/7 is in no way cloase to 3.14159265359.......
though 1/3 is very accurately 0.3 repeating.
I agree that 0.9 repeating is not so true for real life because you will never use that many numbers, but since we are talking about algebra here, I'd have to say 0.9 repeating=1 is algebratically true!