I was wondering is there any way to express $0.999999$ recurring as an actual fraction without equaling $1$? Because I tried to convert it into a fraction following the rules for normal recurring decimals like this:
But as you can see the result is $9/9$ which ultimately is equal to $1$ . And I've even tried calculating it other ways like this:
But it always ends up telling me that $0.9999999... = 1$. Is there any mistake in my logic? And I also realized this applied to other recurring decimals ending in $9$. E.g: $0.5999999...=5.4/9 = 0.6$ . So is there a way to write $0.999999...$ as a fraction so you can differentiate it from $1$?