# Irrational numbers helpWatch

#1
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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5 months ago
#2
Root 2 is not a recurring decimal that’s why
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5 months ago
#3
(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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#4
(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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5 months ago
#5
(Original post by yusyus)
how can they prove that though?
does that mean recurring decimals aren't irrational?
Recurring decimals are rational numbers.
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#6
(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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5 months ago
#7
(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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5 months ago
#8
(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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