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Change of base calculations

  1. Dec 5, 2013 #1
    1. The problem statement, all variables and given/known data

    1. Convert (0.333...)4to base 10.

    2. Convert (0.333...)10to base 4.

    2. Relevant equations

    For question 1:


    I see this can be written as (3/4+3/42+3/43...)10

    Can I just use the geometric formula and arrive at the answer 12/3=4 ?

    But that doesn't match, because 4 in base 10, written in base 4 is just 10.




    For problem 2 I'm not sure how to start. There was a trick regarding division and keeping the remainder, but I'm not sure that applies to decimals.


    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 5, 2013 #2

    tiny-tim

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    hi srfriggen! :smile:
    yes, but doesn't your formula apply to 1 + 3/4 + … ? :wink:

    (btw, doesn't that look a lot to you like 0.9999… ?)
    you mean to quaternary? (quaternals?)

    yes, long division works in any system :smile:
     
  4. Dec 5, 2013 #3
    the series can be written as 3*10-1+3*10-2+3*10-3...

    And isn't the formula for a geometric series: a(1/1-r)?

    So here, a=3 and r=1/4, right?

    When I plug in and multiply out I get an answer or 4, not .9...

    What am I missing?
     
  5. Dec 5, 2013 #4

    tiny-tim

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    3*1 + 3*10-1+3*10-2+3*10-3...= a(1/1-r) :wink:
     
  6. Dec 5, 2013 #5
    Wait, I wrote that out wrong, it's not:

    he series can be written as 3*10-1+3*10-2+3*10-3...

    those 10s should be replaced with 4s, right?


    I'm still getting a=3 and r=1/4. Am I right with that?
     
  7. Dec 5, 2013 #6

    tiny-tim

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    a*(1 + b + b2 + b3) + … = a/(1 - b)

    you left out the a*1 (= 3), which if you subtract from 4 is …? :wink:
     
  8. Dec 5, 2013 #7
    so isn't the formula a=3 and b=1/4? If so that still give the answer or 4. I don't see where subtracting 3 comes into play.
     
  9. Dec 5, 2013 #8

    tiny-tim

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    your formula does not have an a*1 …

    it starts with a*b :smile:
     
  10. Dec 5, 2013 #9
    I'm looking at my book now and it says the formula is a(1/1-r). If a=3 and r=1/4, I get the answer to 4. I'm not sure what is wrong of the previous statement? Either my formula is wrong or my a and r choices are wrong.
     
  11. Dec 5, 2013 #10
    I'm sorry tiny tim I'm just not getting it today. I'm gonna take a break, so some studying later, and come back to this one. Thanks for your patience so far!
     
  12. Dec 5, 2013 #11

    tiny-tim

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    a*(1 + b + b2 + b3 + …) = a/(1 - b) = 3/(1 - 1/4) = 4

    a*(b + b2 + b3 + …) = a/(1 - b) - a = ab/(1 - b) = 4 - 3 = 1
     
  13. Dec 5, 2013 #12
    ahhh, now I see what you meant by "your formula" !
     
  14. Dec 5, 2013 #13

    tiny-tim

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    ok, alternative method: can you see that 0.33333 = 1 - 0.00000… ?

    (ie you can't get any closer to 1 ! :wink:)
     
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