Pretty much. One of the limitations of a base 10 number system is that it sucks at dealing with the number 3.
0.999... is the same as writing something as 3/3 or 9/9 or 999/999.
People think that because they look different, they can't mean the same thing. We do it with language all the time:
1 = I = One = Uno = Ichi = 9/9 = 0.999...
This is like saying sky blue is close enough to navy blue, and so they're both just 'blue'
For some purposes, yes, it's close enough. But they are unique values and this means you can't munge them except in specific contexts.
0.9 repeating is exactly, precisely equal to 1. They are exactly, precisely the same number. This can be unintuitive, but stems from the definition of real numbers. Two real numbers are different numbers if they have an infinitely many of numbers between them. These two numbers don't, so they are the same number.
Also:
0.9...=0.9... |×10
10×0.9...=9.9...|-0.9...
9×0.9...=9|÷9
0.9...=1
ALSO we can define 0.9... as the sum of the infinite geometric series where the n:th member of the series is defined as 0.9×(1/10)^(n-1). The sum of infinite geometric series is exactly known (when they converge), and for this series (that is 0.9...) it is precisely 1.
0.9... is not "for all intents and purposes" equal to 1. It is EXACTLY equal to 1.
0.999... =/= 1
but
0.999... ~ 1
You can also write the number 1 as an infinite series, like 1/2 + 1/4 + 1/8 + 1/16 + ... = 1
>1/9 = ~ 0.111...
it just depends how close you really want to get
is like how you put 0 after 1 to make 9 10
ALSO also: there's a whole Wikipedia article on this shit en.m.wikipedia.org
ALSO ALSO: the intuitive confusion around the subject comes from the inability to cope with infinity and the unwillingness to accept that there can be many was to represent the same number. Just like I can write 2×4=8 where 2×4 is exactly the same thing as 8, I can write 0.9...=1 it's just two different was of writing the same number. If there's nothing between the two numbers (and there isn't, a number like 0.0...1 doesn't exist because that's not how infinity or infinitesimals work), they have to be the same number.
The real number line is infinitely dense, so all different points on it are separated by infinitely many points. 0.9... and 1 don't have infinitely many numbers between them, so they have no numbers between them.
0.9999...≠1 implies
0.9999...>x
1/3 = 0.333...
2/3 = 0.666...
3/3 = 0.999... = 1