One method which I find easier is converting both into fractions.
8/9 = 8/9 , and 0.9 = 9/10
Now, you have to find the least common denominator, which is 90 (9*10)
Now you have 80/90 and 81/90.
You have finished 80/90.
Your friend has finished 81/90.
81/90 > 80/90 so your friend is correct, they have done more of their project.