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.999=x
10x=9.999
10x - x = 9x
9x=9
1x=1.
.999 = 1.
And your first problem has a mistake.
10 * .999 = 9.99
and
10x - x = 8.991 not 9
As i mentioned before actually going into the math, it was to be understood that .999 was .9 repeating.
.9 repeating, times 10, would in fact be 9.9 repeating right?
[edit on 24-3-2005 by The Vagabond]
Originally posted by American Mad Man
the problem with your 1/3 x 3 is that is not how it should be stated. If you are representing in fractions of 3, the number "3" is not stated correctly.
thus, 1/3 x 3 should be expressed 1/3 x 9/3, or 1.
For 10x (where x=.9 repeating), you have:
10x - x= 9x
then you have:
9x=9
this is wrong.
You are solving the multiplication first instead of the addition (or subtraction).
Originally posted by Crysstaafur
.999=x Inits
10x=9.999 Multiplied by 10 on both sides.
10x - x = 9x Opps.... While the statement is true it is a non-connected system not in relation to the former operation...
Originally posted by Crysstaafur
.999=x Inits Legal
10x=9.999 Multiplied by 10 on both sides. Legal
10x - x = 9x Opps.... While the statement is true it is a non-connected system not in relation to the former operation.. Not Legal
In the above, you have completely disregarded the repeating 9.
The only thing achieved here is a separate equation that says
(Unknown multiplied by 10) subtracting an unknown of simular scale should yield
Unknown multiplied by 9. Unrelated.
If you were trying to include an x on the repeating side, you would wind up
multiplying 10x by x which would be 10x^2
ergo
10x=9.999 Multiplied by 10 on both sides. Legal
10x^2 = 9.999x Multiplied by x on both sides. Legal
The big gotcha was the disregard for the repeating 9. simple.
Imaginary (all off on it's own, based on the impossiblity to simplify square root of -1)