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Thread: rational and irrational

  1. #1 rational and irrational 
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    how do you distinguish an irrational fraction from a rational number.
    in rational fraction the pattern is repeated after say x number of digits.
    but in irrational fraction we say the pattern does not repeat. how can we say this before looking for say thousand decimal places, maybe a million digits.
    is there no simpler method to know whether a fraction is rational or irrational


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  3. #2  
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    You can prove logically that specific numbers are irrational (pi, e, etc.) . Just google "proof that ____ is irrational" and you will find many proofs with whatever irrational number you are curious about.


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  4. #3  
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    Decimal expansions are bad way of telling rational numbers and irrational numbers. You might have a expansion that appears no pattern but after the millionth decimal place starts repeating regularly. But equally you can have an expansion that appears to repeat but after the millionth decimal place becomes totally random. Unless a number is written explicitly as a recurring decimal (e.g. ) itís best not to have nothing to do with decimal expansions as a way of sorting out the rationals and the irrationals.

    There is more to rational and irrational numbers than just decimal expansions. Try and learn more about them.
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  5. #4 Re: rational and irrational 
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    Quote Originally Posted by parag1973
    how do you distinguish an irrational fraction from a rational number.
    in rational fraction the pattern is repeated after say x number of digits.
    but in irrational fraction we say the pattern does not repeat. how can we say this before looking for say thousand decimal places, maybe a million digits.
    is there no simpler method to know whether a fraction is rational or irrational
    As Jane said, decimals are a poor way to look at the question. When you use the word "fraction" you have almost gotten to the definition of a rational number which is simply a number of the form n/m where n and m are integers. That is the form in which most mathematicians use rational numbers.

    An irrational number is a real number than cannot be expressed as a ratio of two integers. You might find it interesting to prove for yourself that is irrational. Hint: Assume it is rational, express it as a ratio of two integers with no common factors, and derive a contradiction.
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  6. #5 topic of rational and irrational numbers 
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    An irrational number is a real number than cannot be expressed as a ratio of two integers. You might find it interesting to prove for yourself that is irrational. Hint: Assume it is rational, express it as a ratio of two integers with no common factors, and derive a contradiction
    In rational fraction the pattern is repeated after say x number of digits.
    but in irrational fraction we say the pattern does not repeat. how can we say this before looking for say thousand decimal places, maybe a million digits.
    is there no simpler method to know whether a fraction is rational or irrational.
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  7. #6 Re: rational and irrational 
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    The irrational fraction believes in UFOs and the yeti.
    "First we build the tools, then they build us" - Marshall McLuhan.
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