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Irrational numbers help

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
Root 2 is not a recurring decimal that’s why
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.
Reply 3
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yusyus
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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?
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
Reply 5
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yusyus
OP
21
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
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.
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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