Question

What is .9999 repeating as a fraction?
.1111?

Answer 1

Are these different questions?
What is .999... repeating as a fraction?
What is .111... repeating as a fraction?

Answer 2

I was wondering the same thing

Answer 3

@MLCochenour

Answer 4

@AccessDenied @Xmoses1 yes these are different questions

Answer 5

For your first one, consider that each 9 is divisible by 3
If we divided it, we'd have
.9999... / 3 = .3333 ...
Do you know a fraction that has this type of decimal?

Answer 6

@AccessDenied sadly I do not

Answer 7

Alright. This one is actually 1/3. But I'll reword a justification that might reinforce what I am getting at.
.9999 ... / 3 = 1/3 is what we just stated. The 3' s then would cancel and we get this statement:
.9999... = 1
So, at first glance, this looks weird. You have what appears to be a decimal less than 1 equal to 1.

Answer 8

But the fact that there are infinitely many 9's repeating there, the reasoning is that .9999... repeating is so close to 1 that there is no difference.
Say, you took 1 - .9999... . you'd think there would be a .00001 somewhere, but it only keeps going. there is no actual termination of 1.

Answer 9

Yeah, that looks very weird @AccessDenied

Answer 10

and if it is hard to believe, you're not alone. A lot of people find it hard to believe too.
there's quite a bit of stuff on the idea, here's the wikipedia article on it if it is at all interesting.
http://en.wikipedia.org/wiki/0.999...

Answer 11

But in the end, our fraction is really .9999... = 1/1.

Answer 12

As for .1111.. repeating, if we were to multiply 9/9 to it, which is the same as multiplying 1, the identity...
.1111 * 9 / 9
Notice that we just multiply all those 1's by 9. You get that same mystical looking decimal again.
.9999... / 9
We already said it was .999... = 1
1 / 9

Answer 13

If you used long division you could show both too:
1/1:
. 9 9 9 9 9 9 ....
1 / 1 . 0 0 0 0 0 0
- 9
1. 0
- 9
and so on.
1/9
. 1 1 1 1 1. ...
9 / 1 . 0 0
- 9
1 0
- 9
1 and so on again.