DoubtProve the term is irrational

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    Irrational Term
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Homework Help Overview

The discussion revolves around the nature of a specific number characterized by having zeroes in all decimal places at intervals of 10^n. The original poster expresses uncertainty about whether such a number can be classified as irrational.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to reason that the lack of a definite pattern in the placement of zeroes suggests the number cannot be expressed as a rational number. Some participants question the periodicity of the number's decimal expansion, suggesting that all rational numbers must have periodic expansions.

Discussion Status

Participants are exploring the implications of periodicity on the classification of the number. There is acknowledgment of the original poster's concerns, and some guidance is provided regarding the reasoning behind why the number cannot be periodic. However, there is no explicit consensus reached in the discussion.

Contextual Notes

Participants note that the original poster is seeking a simpler explanation of the concepts involved, indicating a potential gap in understanding the definitions of rational and irrational numbers.

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Homework Statement


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 I am still not sure about it)


Homework Equations





The Attempt at a Solution


when i think about it,since the number of zeroes don't 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?
 
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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.
 
Dick said:
u haz allreddy said everythin it cnt be peridic, cn it? all rationals haz peridcic expanshions. Maybe I forgot to misspell something there, sorry.
Fantastical reply, Dick !
 
thanx!

Ohk...Thanx guyz... :)
(still somthings buggin me though )
 
vio said:
Ohk...Thanx guyz... :)
(still somthings buggin me though )

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.
 
SammyS said:
Fantastical reply, Dick !

Thanks. It was hard to resist...
 

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