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- Thread starter VashtiMaiden
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- #2

nicksauce

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If you can write z = x/y where x and y are integers, then z is rational. Otherwise z is irrational.

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is pi rational?

- #4

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is .66666..... rational? why?

- #5

nicksauce

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Is .66666.... rational? Can you think of a fraction that gives .666666... ? I would hope you can.

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ok, thanks nicksauce

- #7

lurflurf

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a real nummber x is rational if and only if its decimal expansion at some point repeats.

let () be repeat this sequence

1/9=.(1) so rational

8134808921309.2872918752801(29148991280409) so rational

pi has no such patern, though this is not obvious

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ah, ok,

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Little off-topic, but here goes: I'm curious, is this not true in some integer base?for decimal form a useful fact is

a real nummber x is rational if and only if its decimal expansion at some point repeats.

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HallsofIvy

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If you mean "is it true in **any** integer base", yes.

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- #12

lurflurf

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Sorry noLittle off-topic, but here goes: I'm curious, is this not true in some integer base?

in base pi

pi which is irrational=10

4 which is rational=10.220122021

a problem with algebraic bases

in base root-2

root 2=10

2=100

- #13

HallsofIvy

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Did you miss the word "integer" in "integer base"?