Find the complement using base 9

I have this simple problem which for some reason I have trouble with I'll be glad to get help.

I have these two numbers in base 10 :

5250, 321.

I change the basis from 10 to 9 then I get :

5250 --> 7173

321 ---> 386

I use the method of r complement with base 9:

First of all I'll find the the complement of 0386 in base 9 which is 6561-386=6175.

Therefore :

7173+6175=14358 (in base 9)

since its a complement to 9, we receive 4358 in base 9

Which is incorrect.

Any ideas why my method is incorrect?

Any help will be appreciated.

Solution

you are mixing bases. 6561 is base 10 for 10000 in base 9.

You need to calculate 100000 - 386 in base 9 to get the complement. This results in 88503. So 88503 is the 10's complement of 386 in base 9. Note the extra digit, otherwise 7173 will be a negative number in this representation.

Now you can calculate 7173 + 88503 = 106676. So the result is 6676 which is 4929 in decimal, which is the expected result.