Is this really true?
The idea is that 0.9 recurring
(0.999... with the digits going on forever)
is actually equal to 1
(Here we write 0.999... as notation for 0.9 recurring, some people put a little dot above the 9, or a line on top like this: 0.9)
Does 0.999... = 1 ?
Let us start by having X = 0.999...
X = 0.999...
10X = 9.999...
Subtract X from each side to give us:
9X = 9.999... − X
but we know that X is 0.999..., so:
9X = 9.999... − 0.999...
9X = 9
Divide both sides by 9:
X = 1
But hang on a moment I thought we said X was equal to 0.999... ?
Yes, it does, but from our calculations X is also equal to 1, so:
X = 0.999... = 1
0.999... = 1
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