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maslam

pakistan
Joined: Jul 4, 2006
Posts: 2
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real numbers

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i m confusing about rational & irrational numbers. i got some idea but still not clear.e.g numbers like 1/3 are rational or irrational as it is in the form of quotient of integers which shows that it is rational but its decimal form is non terminating which is a contradiction to the definition of rational numer.

[Jul 20, 2006 12:00:09 PM]

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pskinner

Joined: Apr 2, 2005
Posts: 797
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Re: real numbers

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Well, the way I like to look at it is this: if a number can be expressed as a ratio of integers, then it is rational. The fact that 1/3 has a nonterminating decimal does not interfere with that way of looking at things. (Besides, that's the definition of a number being rational.)

But, there is really more going on here. The fact is that nonterminating decimals that "repeat", like .333..., can be shown to be equivalent to ratios of integers while nonterminating decimals that do not repeat can be shown to not be able to be expressed as ratios of integers. Of course, these require "mathematical proof" which goes a bit beyond, but if you ask, I'll show you the proof of why the nonterminating decimal .333... is, in fact, 1/3. The proof that nonterminating decimals that do not repeat are irrational is more advanced.

Hope this explains what is going on.
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Principal Skinner

[Jul 20, 2006 7:06:48 PM]

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