DoubtProve the term is irrational

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    Irrational Term
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The discussion centers on proving that a number composed solely of zeroes in decimal places defined by 10^n is irrational. Participants argue that since the placement of zeroes does not follow a periodic pattern, the number cannot be expressed as a fraction, which is a requirement for rationality. The inability to identify a repeating sequence of digits further supports the claim of irrationality. One contributor emphasizes that if a number were rational, it would eventually exhibit a periodic pattern, which is not the case here. Overall, the consensus is that the non-periodic nature of the number's decimal expansion confirms its irrationality.
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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)


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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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