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Homework Help: Tersonian decimal expansion?

  1. May 1, 2010 #1
    1. The problem statement, all variables and given/known data

    1/7=?


    2. Relevant equations



    3. The attempt at a solution

    Consider $$y=\overline{145827}.0=\dots145827145827145827.0$$,
    then $$1000000y=\dots 145827145827000000.0$$ and $$-999999y=145827$$ .
    Therefore, $$y=-\dfrac{145827}{999999}$$ . Son in fact $$\overline{145827}.0$$ is a "negative" number.

    $$\dfrac{1}{7}=-\overline{145827}.0$$ However, There is no minus in Tersonian decimal expansions?? How can I show 1/7 in Tersonian decimal expansion??
     
  2. jcsd
  3. May 1, 2010 #2

    tiny-tim

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    Science Advisor
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    Welcome to PF!

    Hi matal! Welcome to PF! :smile:

    What's "Tersonian" ? :confused:

    (I couldn't find it in wikipedia or google)
     
  4. May 1, 2010 #3
    yes, I searched it too. My teacher said "Here are some problems from Tersonian Elementary School Mathematics Book:" For instance , y=\overline{12}.0 is a Tersonian decimal expansion. Normally, decimal expansions are in after the comma but in tersonian, expansions in before the comma.
     
  5. May 1, 2010 #4
    You mean neither of you watch star trek??!

    Should 145827 read 142857 or is that part of the problem too?
     
  6. May 1, 2010 #5
    145827 is not part of the problem. for instance, when you show -1 in tersonian decimal expansion:
    you should write " consider a number y= \overline{9}.0=\dots9999.0 . Then 10y= \dots 9990.0 and -9y=9 . Therefore y=-1 so -1=\overline{9}.0" I mean I need a tersonian decimal expansion which equals to 1/7.
     
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