so i know the proof and answer for this but can you try and prove this? don't go and look it up, because that would be cheating.
prove that 0.99999999999999999999... = 1
go on, give it a shot!
x = .999999.....
10x = 9.9999999...
10x-x = 9x
9.99999.... - .99999... = 9x
yup that's the same proof i got :D