# Is this really true?

The idea is that 0.9 recurring

(0.999... with the digits going on forever)

is actually equal to 1

(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

And so:

0.999... = 1

*Does anyone disagree with this? Let me
know on the Math is Fun Forum.*