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 $481$?????  

As I explained in 2011, one easy way is to write the number in Horner form in the original base, then do the base conversion from the inside-out, e.g. below where $\rm\color{#c00}{red}$ means radix $9$ notation
$$\begin{align} 397 
\,&=\, (3\cdot 10\, +\, 9)\,10 +7\\
&=\, (\color{#c00}{3\cdot 11+10})10+7\\
&=\qquad\quad\ \  \color{#c00}{43\cdot 11}+7\\
&=\qquad\qquad\ \ \ \color{#c00}{473}+7\\
&=\qquad\qquad\ \ \ \color{#c00}{481}\end{align}$$
