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Base 10

  1. May 6, 2004 #1
    I know that our current decimal system has a base ten.

    My question is, how can i figure out fractions to decimals with different bases?

    basically, i would like to know how to use different bases other than 10.
     
  2. jcsd
  3. May 6, 2004 #2

    chroot

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    You'd use long-division, just like you've always done in decimal.

    Consider the following division problem in binary, which has only digits: 0 and 1.

    100000 / 1000

    Set up your long division as usual:
    Code (Text):

         ______1__        
    1000 |  100000
          - 1000
          ---------
            000000
     
    Of course, this makes sense: 1000 in binary is 8 in decimal. 100000 in binary is 32 in decimal. 32 / 8 = 4, or 100 in binary.

    All of the normal division, multiplication, addition, and subtraction algorithms you learned in grade school work exactly the same way in any base.

    If you have a specific question you're trying to solve, please let me know, and I'll help you.

    - Warren
     
  4. May 8, 2004 #3
    if i have a # like 1/9 (base 10) and i want to fine what it equals with base 5...How would i go about doing that?
     
  5. May 8, 2004 #4

    Integral

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    Using base 10 arithmetic, multiply your decimal number by the new base. The integer part is a digit in the new base. Repeat the process with the fractional part. Each repetition generates the next digit.

    For example .1 in base 10 to base 2

    2*.1 = 0.2

    integer part =0 so your first digit is 0
    .110~ .02

    Now take the fractional part and repeat.
    2 *.2 = 0.4
    .110~ .002

    repeat
    2*.4 =0.8
    .110~ .0002

    repeat
    2*.8 = 1.6
    Finally! a non zero digit!
    .110~ .00012

    2*.6= 1.2
    .110~ .000112

    2*.2=0.4
    .110~ .0001102

    now you can observe that a pattern is emerging.

    This same method can be used for conversion to any base.
     
    Last edited: May 8, 2004
  6. May 8, 2004 #5
    thanks alot
     
  7. May 10, 2004 #6
    so would .1 (base 10) equal .021262 and so fourth in base 5?
     
  8. May 10, 2004 #7

    jcsd

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    No, 0.1 in base 5 would equal [itex]0.\dot{2}[/itex]. Remember base 5 would only use the digits 0, 1, 2, 3 and 4 so that 6 can't be in there.
     
  9. May 10, 2004 #8
    hmm....

    can you show me you work for that?

    For some reason im having trouble..
     
  10. May 11, 2004 #9

    jcsd

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    Sorry I left out a zero, it should be : [itex]0.0\dot{2}_5[/itex] (out of interest ([itex]0.\dot{2}_5[/itex] would be equal to a half). As Chroot says use long divison (I'll state all numbers in base 10 unless otherwise indicated by a subscript 5, also I've used fractions rather than decimals as I feel it's probably easier to see what's going on)

    (1/10)/(1/5) = 0 R 1/10
    (1/10)/(1/25) = 2 R 1/50
    (1/50)/(1/125) = 2 R 1/250
    (1/250)/(1/625) = 2 R 1/1250
    (1/1250)/(1/3125) = 2 R 1/6250

    That gives us so far 0.022225 + 1/6250

    Now we've probably already guessed that this is going to be a a recurring number, infact we should of seen this about the begining as 1/10 = (1/5)(1/2) and x in the equation [itex] \frac{x}{5^n} = \frac{1}{2}[/itex] can never be an integer.
     
  11. May 13, 2004 #10
    alright, thx
     
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