<s>[INST] 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 $481$?????  
 [/INST] You cannot simply keep the same coefficients but change the $10$'s to $9$'s. What you must do is something like the following:
$$\begin{align}397&=3\times \color{red}{10}^2+9\times\color{red} {10}^1+7\times \color{red}{10}^0\\&=3\times(9+1)^2+9\times(9+1)+7\times 1\\&=3\times\color{blue}9^2+(3\times18+3)+\color{blue}9^2+\color{blue}9^1+(7)\\&=4\times \color{blue}9^2+(6\times9)+(10)+\color{blue}9^1\\&=4\times \color{blue}9^2+8\times \color{blue}9^1+1\times \color{blue}9^0\end{align}$$
What you did was simply change the tens in red to nines without doing any intermediate steps.
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