Is 8 over 9 greater than 0.789?

Yes.

Convert to the same format then a comparison can be made:

To decimal:

8/9 = 8 ÷ 9 = 0.888.... > 0.789 → 8/9 > 0.789

To fractions:

0.789 = 789/1000

8/9 = 8000/9000

789/1000 = 7101/9000

8000 > 7101 → 8000/9000 > 7101/9000 → 8/9 > 0.789