03112011, 03:03 PM
Quote:
Originally Posted by reuben2011
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.

That's one of the algebraic methods mathematicians use to prove it.
There's also the idea that 0.9 repeating gets closer and closer to 1, but never quite reaches it.
Last edited by debussybunny563; 12212012 at 12:00 AM.

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