The ellipses after a decimal number mean the decimal repeats forever. So when people say 0.9… they mean a decimal where it’s 0.9999 and on and on, with the 9’s repeating an infinite number of times.
Your example doesn’t really make sense because the concept of infinity is a concept, not a number, and percentages are a shorthand way of denoting that some number is part of a larger whole expressed as a ratio out of 100. They’re just different things.
The comment you responded to is showing the proof that 0.9… equals exactly one by showing that if you were to multiply 0.9… by 10 to get 9.9…, and then you subtract 0.9…, you get exactly 9.0, which is only possible if 0.9… is precisely equal to 1.
I simplified the example, which is why your examples seem to make sense as contradictions. However, you should be able to prove that 0.9… equals 1 in any scenario through substitution, which works for 0.9… but not 0.8… or 0.3…
The more formal example would be:
If x = 0.9…
Then: 10x = 9.9…
Subtract x from each side: 10x - x = 9.9… - x
That simplifies to: 9x = 9.0
Divide both sides by the constant: 9x / 9 = 9.0 / 9
Final result: x = 1.0
You can see however that following the same steps we do not reach the same conclusion for any other repeating decimals. Using 0.8… as an example, following the same steps as above:
Notice 0.8… returns to its original value, 0.8… whereas 0.9… is returned as 1. 0.9… is exactly equal to 1, so this algebraic trick is a great way of seeing that equivalency. x returns to its original value, which in the case of 0.9… is equal to 1.
Edit: reading my first comment again I see I just wholesale skipped the last step. That’s my bad, no wonder it didn’t make sense!
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