Is 0.09 greater than 0.1

No, it is smaller because if you rounded 0.09 to the nearest 0.1, you would get 0.1, and another reason you can say it is smaller is because if you put it in fractional terms, 0.09 would look like

9/100, but with 0.1, it would be 10/100, so from that, you can hopefully and clearly see that 0.09 is SMALLER that 0.1