DoubtProve the term is irrational

[vio]

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?

 

[Dick]

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

 

[SammyS]

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 !

 

[vio]

thanx!

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

 

[Dick]

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.

 

[Dick]

Fantastical reply, Dick !

Thanks. It was hard to resist...