1:9=0.111111111...
2:9=0.222222222...
3:9=0.333333333...
...
8:9=0.888888888...

So, why 9:9=1?
Shouldn't it be 0.999999999...
Shouldn't it be a little less than 1?

(8:9)+(1:9)=(9:9)

8:9= 0.888888888...
and 1:9= 0.111111111...
So 9:9= 0.888888888...+0.111111111...=0.999999999...

If 9:9=1, than 8:9= 0.888888889, which is not true...
Or than, 1:9= 0.111111112, which is also not true...

Can anyone solve this problem?

0.9999999... = 1

There are two ways to express every number (and that is usually a problem to define the real numbers), for example:
23.49999999... = 23.5

To show that:
a=0.9999...
10a=9.99999...
10a-a=9
9a=9
a=1

Another way of the proof is:
0.9=9/10
0.99=9/10+9/100
0.999=9/10+9/100+9/1000
and when you write:
0.9999999... that is equal to
9(1/10+1/100+1/1000+...) and that sum converges to 1!

So the answer of the question about if 9/9 is 1 or 0.99999, is both, and both are the same.

PD: Im learning English, so this comment is a practice of my English. I expect it is ok!.

0.9999...=1
1:9=0.1111, (1:9)×９＝１
so （１：９）×９＝(0.1111...)×9=0.9999...=1

u can say its a maths magic....:)

Thanks everyone. Your english is good Mauricio, so is your math! Yours to, Leon. Yes Pearl, math is magic! Take care everyone.