The problem is, that’s exactly what the … is for. It is a little weird to our heads, granted, but it does allow the conversion. 0.33 is not the same thing as 0.333… The first is close to one third. The second one is one third. It’s how we express things as a decimal that don’t cleanly map to base ten. It may look funky, but it works.

???

Not sure what you’re aiming for. It proves that the setup works, I suppose.

x = 0.555…

10x = 5.555…

10x = 5 + 0.555…

10x = 5+x

9x = 5

x = 5/9

5/9 = 0.555…

So it shows that this approach will indeed provide a result for x that matches what x is supposed to be.

Hopefully it helped?