Conversion to base $9$ Where am I going wrong in converting $397$ into a number with base $9$?
$397$ with base $10$ $$= 3 \cdot 10^2 + 9 \cdot 10^1 + 7 \cdot 10^0$$  To convert it into a number with base $9$ 
$$3 \cdot 9^2 + 9 \cdot 9^1 + 7 \cdot 9^0 = 243 + 81 + 7  = 331$$
But answer is $481$?????  

$481_{[9]} = 4\,\cdot\,81 +8\,\cdot9+1\,\cdot\,1 = 324 + 72 + 1 = 397_{[10]}$
The conversion you presented is incorrect, you converted $397_{[9]}$ into $331_{[10]}$, which is not what you want.
To convert it properly:
$397/9 = 44$ (remainder = $1$)
$44/9 = 4$ (remainder = $8$)
$4/9 = 0$ (remainder = $4$)
The remainders give the result: $\boxed{397_{[10]}=481_{[9]}}$
