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Ternary expansion

  1. Oct 31, 2011 #1
    Hi guys, I'd like to ask about ternary expansions. they seem easy but i'm having a hard time doing this as well as searching for tips online, specifically for [tex]x \in [0,1][/tex].

    I know that ternary expansions are similar to decimal expansions but for example, how do you find the ternary expansion of [tex]\frac{5}{3^3}[/tex] ?
  2. jcsd
  3. Oct 31, 2011 #2


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    In base 3, 5= 3+2 is [itex]12_5[/itex]. Of course, [itex]9= 3^2[/itex] is [itex]200_3[/itex] so the fraction 5/9, in base 3, would be the fraction [itex]12/200[/itex]. Can you write that in "trinary"?
  4. Oct 31, 2011 #3
    Hi hallsofivy, sorry I didnt quite understand your reply.

    And oh, it's 5/27 not 5/9. Perhaps a better way of explaining it to me would be how to identify the coefficients [tex]a_k[/tex] such that [tex]\frac{5}{27} = \sum \frac{a_k}{3^k}[/tex] ?
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