# 0.999 = 1 (Why?)

0.999.... = 1 (Why?)

Sorry to put such a basic question on here, but it's not for homework so I figured I'd post here.

On these forums, I've saw the issue of .99... = 1 brought up before; however, I recently discovered it in Math class.

My teacher said it equals one because it is being rounded; however, it actually doesn't equal one. I understand what she means; however, for some reason, I recall seeing a formula that mathematically proved .99... = 1 without rounding. Perhaps I am seeing things.

That formula (or the closest thing to it, there is no formula) is in those fifty other threads.

Icebreaker
If your teacher said that 0.999... is only approximately 1, then she is wrong.

Tom Mattson
Staff Emeritus
Gold Member
Dooga Blackrazor said:
My teacher said it equals one because it is being rounded; however, it actually doesn't equal one.

Quickie demonstration:

$$\frac{1}{3}=0.\bar{3}$$

$$3\left(\frac{1}{3}\right)=3(0.\bar{3})$$

$$1=0.\bar{9}$$

And if your teacher still thinks that $0.\bar{9}=1$, then ask him/her to try to find a real number between the two. It can't be done.

Integral
Staff Emeritus
Gold Member
HallsofIvy