Simpler way to Convert base 3 to base 9 than going through base 10

Question

anonymous · Answer

@jim_thompson5910

anonymous · Answer

$$11110212.20211_3= 3263.757202_{10}$$

anonymous · Answer

then $$3263_{10} = 4425_9$$

and then the decimal part

anonymous · Answer

@jim_thompson5910  how does fractions work?


i know you multiply by the base but how long do you do for ?

jim_thompson5910 · Answer

ganeshie8 · Answer

Notice that  $\large 9^k =   3^{2k}$

ganeshie8 · Answer

So a number taking "k" bits in base 9 takes exactly 2k bits in base 3

anonymous · Answer

i llooked at his work he just splits it up into 2 bits

ganeshie8 · Answer

$$\large \left(11110212\right)_3  = \left(\overline{11}~\overline{11}~\overline{02}~\overline{12}\right)_3 = \left(4425\right)_9   $$

anonymous · Answer

|dw:1410840030206:dw|