Caleb M. answered • 03/27/17
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Mathematics Tutor
If you mean 0.999999, then Mark M.'s answer is correct. However, if you mean 0.9999... (meaning infinitely many 9's) then the answer is surprisingly 1! This can be seen using infinite series in Calculus (this is an infinite geometric series). But there is an easier way of seeing this. Let x=0.9999... But then 10x=9.999999.... Let's write these on top of each other:
10x=9.999999...
x=0.99999...
We subtract these two equations and get 9x=9 (as 10x-x=9x and 9.9999....-0.99999...=9) so that x=1. But x=0.99999... so that 0.99999=1. Similarly, 2.99999....=3, -1.999999=-2, etc.
