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#1 2011-11-27 03:55:44
- kumara
- Member
- Registered: 2011-11-25
- Posts: 7
irrational nuumbers
how to identify irrational numbers ? are there any rules? please help me
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#2 2011-11-27 05:30:56
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: irrational nuumbers
Hi kumara;
I answered this question for you already in the other thread.
http://www.mathisfunforum.com/viewtopic … 72#p195572
Post #2813.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#3 2011-11-29 02:04:15
- kumara
- Member
- Registered: 2011-11-25
- Posts: 7
Re: irrational nuumbers
please give one example for that bobbym
Last edited by kumara (2011-11-29 02:05:13)
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#4 2011-11-29 02:25:38
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: irrational nuumbers
A rational number has a finite continued fraction, it will terminate.
An irrational has a non terminating continued fraction. Meaning it never ends.
The 2 continues on forever and this simple continued fraction is written:
The 2,4 continues on forever and this simple continued fraction is written:
These that are irrational and have a repeating pattern are called quadratic irrationals.
Of course it was easy with the square roots because when we see them we know they are irrational but how about pi?
It never ends and there is no pattern like 2,4,2,4,2,4. Therefore this number is not rational.
How about the golden ratio, this is not so easy to prove it is not rational. But looking at its continued fraction we see that it is a quadratic irrational. So it is not rational.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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