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Homework Help: 0.541 recurring as a fraction

  1. May 11, 2010 #1
    What is 0.541r as a fraction? I have a feeling the answer won't be as simple as 541/1000.
     
  2. jcsd
  3. May 11, 2010 #2

    Cyosis

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    Homework Helper

    Write it as a sum of 0.541+0.000541+0.000000541+..... and use the geometric series.
     
  4. May 11, 2010 #3
    Thanks Cyosis. I see that the answer would be 541/999.
     
  5. May 11, 2010 #4

    Cyosis

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    Homework Helper

    Yes, that is correct.
     
  6. May 15, 2010 #5
    Hi,
    I was taught what I consider a really neat trick for writing recurring decimals as fractions(supernerdy) and thought I'd share it. :D

    let x = 0.54154141......
    1000x=541.541541......
    1000x-x=541
    999x=541
    x=541/999
    0.541.....=541/999
    :D

    It's probably easier to use Cyosis' method though :D
     
  7. May 15, 2010 #6
    .aaaaaaaaaaaa ... = a/9
    .abababababab ... = ab/99 (ab is not multiplication, simply the digits)
    .abcabcabcabcabc ... = abc/999 (again, not multiplication between a b and c)

    and so on
     
  8. Jun 26, 2010 #7
    0.541r could also be interpreted as radian measure. In which case it might be an approximation of 0.54105 20681 18242 1 = 31 π / 180, or an angle of 31 degrees.
     
  9. Jun 26, 2010 #8
    [tex]
    \begin{array}{rclr}
    x & = & 0.(541) & \. /\cdot 1000 \ (\mathrm{because \, the \, period \, is \, 3 \, decimal \, places \, long}) \\

    1000 x & = & 541.(541) &
    \end{array}
    [/tex]

    Subtract the two equations. What happens to the decimal part? Then solve for x and you should get your answer in a form of a fraction.
     
  10. Jun 26, 2010 #9

    HallsofIvy

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    Yes, it could but given the title of this thread, that is extremely unlikely.
     
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