The greatest nine-digit number that can be made using nine different digits is 987,654,321. Using the number zero only makes the largest possible number smaller.
To create the largest possible nine-digit number, the hundred-millions digit must be the biggest digit. In this case, that number should be nine because it is the largest possible digit. The ten-millions digit should be the second biggest number, or eight in this case. If the number used was seven, for example, the entire nine-digit number would be smaller by ten million. This trend continues, causing each of the different digits to be in descending order.