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x=0.999999...

10x=9.9999999...

10x-x=9

9x=9

x=1

have seen different explanations for this. what is the real reason?

 Mar 8, 2015

Best Answer 

 #1
avatar+23254 
+5

0.9999...  does equal 1

If you don't believe the algebraic explanation, try this:

   --  if 0.9999... doesn't equal 1, then there must be some number between 0.9999... and 1, but what could it        be?  There is no number between 0.9999... and 1, so they must be the same number.

 Mar 9, 2015
 #1
avatar+23254 
+5
Best Answer

0.9999...  does equal 1

If you don't believe the algebraic explanation, try this:

   --  if 0.9999... doesn't equal 1, then there must be some number between 0.9999... and 1, but what could it        be?  There is no number between 0.9999... and 1, so they must be the same number.

geno3141 Mar 9, 2015

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