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reuben2011
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Default 03-11-2011, 12:04 AM

Quote:
Originally Posted by debussybunny563 View Post
I'm interested in your opinion...

Do you think 0.999.... is equal to 1?
I think the point here is that the "..."'s represent a iteration of the digit "9" indefinitely. Therefore you meant .999999999 with an infinite number of 9's afterward, right? So using the algebra I know to convert repeating decimals into fractions:


x = 0.999... //Set x to the decimal:
10x = 9.999... //Multiply by ten on both sides.

10x - x = 9.999... - 0.999... //Used the information above for this
expression

9x = 9 //Simplify (since the repeating decimal part is
the same for both 9.999... and 0.999..., they
cancel out)

x = 1 //Divide by nine on both sides.

Therefore 0.999... is equal to 1.


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