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What is the 2015th decimal number in the division 2015 by 7

  1. Feb 17, 2015 #1
    What is the 2015th decimal number in the division 2015 by 7?

    This is how I did it but is there an simpler way of showing this...

    I did 2015/7 = 287.857142 857142 857142 857142 ...

    As we have a recurring decimal for the numbers 857142, I divided 2015 by 6 which gives me a non finite answer so I then divided 2016 by 6 = 336. Therefore I concluded that the 2016th number must be an 8 and to answer the question which is 2015th number it must be the preceding number in the recurring pattern so it's 2.

    Am I correct please and could anyone explain a clearer or simpler way, if it exist. Thank you :)
     
  2. jcsd
  3. Feb 17, 2015 #2

    BvU

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    By you reasoning, what is the 24th number ?
     
  4. Feb 17, 2015 #3
    As there are 6 numbers in the sequence 857142 and 24/6 = 4 then the 24th number is 2
     
  5. Feb 17, 2015 #4

    BvU

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    So what about the 2016 th number ?
     
  6. Feb 17, 2015 #5
    Well it must be 2 as 2016/24 = 84
     
  7. Feb 17, 2015 #6

    BvU

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    In post #1
     
  8. Feb 17, 2015 #7

    vela

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    Do you see the contradiction in your two results?
     
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