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    Hi.
    I was just wondering why is it that when proving root 2 is irrational you prove it can't have a fractional form with odd numbers.
    But when I did my GCSE's we converted recurring decimals into fractions by x10 then minusing one i.e

    x=0.1111111
    10x= 1.1111111
    9x=1
    x=1/9
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    Root 2 is not a recurring decimal that’s why
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    (Original post by yusyus)
    Hi.
    I was just wondering why is it that when proving root 2 is irrational you prove it can't have a fractional form with odd numbers.
    But when I did my GCSE's we converted recurring decimals into fractions by x10 then minusing one i.e

    x=0.1111111
    10x= 1.1111111
    9x=1
    x=1/9
    "irrational" means "cannot be expressed as p/q for integers p, q (q nonzero)". I'm not sure exactly what you're trying to ask.
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    (Original post by Y11_Maths)
    Root 2 is not a recurring decimal that’s why
    how can they prove that though?
    does that mean recurring decimals aren't irrational?
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    (Original post by yusyus)
    how can they prove that though?
    does that mean recurring decimals aren't irrational?
    Recurring decimals are rational numbers.
    Watch this video it may help you https://youtu.be/LeU4u0Zivok
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    (Original post by Prasiortle)
    "irrational" means "cannot be expressed as p/q for integers p, q (q nonzero)". I'm not sure exactly what you're trying to ask.
    (Original post by Prasiortle)
    "irrational" means "cannot be expressed as p/q for integers p, q (q nonzero)". I'm not sure exactly what you're trying to ask.
    so recurring decimals just arent irrational then? I think I just have my definitions messed up
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    (Original post by yusyus)
    so recurring decimals just arent irrational then? I think I just have my definitions messed up
    1/9 is a fraction so cannot be irrational.
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    (Original post by yusyus)
    so recurring decimals just arent irrational then? I think I just have my definitions messed up
    Rational = can be written as p/q with p, q integers and q nonzero.
    Irrational = cannot be written in that form.

    It is a theorem that if a number is rational, its decimal expansion will either terminate or recur; further, if a number's decimal expansion terminates or recurs, that number will be rational. This theorem is fairly easy to prove if you know some basic number theory.
 
 
 
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