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Me irl
Substitute x with 0.999...
10x = 9.999...
9.999... - 0.999... = 9
9 divided by 9 = 1
x = 1
I explained this to a VCE maths teacher at my school and then a friend of mine, and here are their responses to it:
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Year 12 maths teacher
0.999... is a rounded version of 3/3, just like 0.333... is a rounded number of 1/3
1/3 is the exact value, and anyone who says 0.333... instead of 1/3, or 0.666... instead of 2/3 might as well round it off to 0.67 = 2/3
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Friend (in year 10)
You're wrong because you had to do all of these calculations to make it equal 1.
By itself, 0.999... does not equal 1.
Then again, I wasn't really expecting anything better from them...
A different year 12 maths teacher in my school said this:
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3.14159 is not an exact value of pi, it is a rounded value (this sentence is true).
The exact value of pi is 22/7 (this sentence is false).
Neither of them are exact values of pi, but 3.14159 is closer to pi than 22/7 is.
This post was edited by Hammer_Hdin on May 12 2010 05:34am