Gilb wrote:
here's one that ISN'T WRONG:
0.99999999(recurring)=9x
therefore
x=0.111111111111(recurring)
10x=1.1111111111(recurring)
10x-x=1
9x=1
therefore
0.99999999999(recurring)=1
Yeah, lots o' people have trouble getting their head around that one. There's no number small enough to add to one to get the other, so the two are equal. One of the oddities of real analysis. You can also prove it with fractions.
1/3=0.333(repeated)
1=3/3=0.999(repeated)
The fraction proof is a little quicker, but you really don't need to worry about these kinds of maths until you're taking 400-level college math courses.
The other thing to remember is that 0.9999999(repeating) is a decimal approximation of a rational number.
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