# Why is 0 9 is 1

## 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

And so:

0.999... = 1

Numbers IndexAlgebra Index

Copyright © 2016 MathsIsFun.com

- What is Ethernet HDMI
- What country name ends with x
- How do you create a magazine
- How can we get UK admission
- Has Ireland joined the Francophonie
- Whats the importance of a reconnaissance?no_redirect=1
- Do you think BBC news is impartial
- What were the Nazis socialist or fascist
- What is the hardest thing about dieting
- Why are ethics not important in marketing
- Is Americas constitution better than Australias
- What is over emotion
- What is Niger
- What are the benefits of Test banks
- Are cats inherently evil creatures