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Doubt!Prove the term is irrational!

  1. Mar 16, 2013 #1

    vio

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    1. The problem statement, all variables and given/known data
    Prove that any number with zeroes standing in all decimal places numbered 10^n and only in these places is irrational?(yeah,its the easiet question in my list,but im still not sure about it)


    2. Relevant equations



    3. The attempt at a solution
    when i think about it,since the number of zeroes dont follow a definite pattern,i mean the same pattern,it will be difficult to represent it as a rational,since one never knows the where the next zero is ,or how its repeatin??..since it not periodic,it must be irrational..
    Well,,when i said that to myself,it seems like i waz just reading out sumthn from a text,i still didnt understand it well enough or sumthin..i know its very basic,but can someone explain it in simpler language?
     
  2. jcsd
  3. Mar 16, 2013 #2

    Dick

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    u haz allreddy said everythin it cnt be peridic, cn it? all rationals haz peridcic expanshions. Maybe I forgot to misspell something there, sorry.
     
  4. Mar 16, 2013 #3

    SammyS

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    Fantastical reply, Dick !!!!!!!!!!!!
     
  5. Mar 16, 2013 #4

    vio

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    thanx!

    Ohk...Thanx guyz... :)
    (still somthings buggin me though )
     
  6. Mar 16, 2013 #5

    Dick

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    Maybe just spelling out why it can't be periodic? If it's rational and it contains a zero digit that zero digit will repeat at some period p once you get into the repeating part. Pick n so that 10^n>p. Then the digits between 10^n and 10^(n+1) will have no zero digits. But there's more than p of them. So it can't be periodic.
     
  7. Mar 16, 2013 #6

    Dick

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    Thanks. It was hard to resist...
     
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