Question

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

Answer 1

@jim_thompson5910

Answer 2

\[11110212.20211_3= 3263.757202_{10}\]

Answer 3

then \[3263_{10} = 4425_9\]

and then the decimal part

Answer 4

@jim_thompson5910 how does fractions work?


i know you multiply by the base but how long do you do for ?

Answer 5

I'm not sure since it's been a while, but this article may help

http://mathforum.org/library/drmath/view/55744.html

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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