More amazing maths

Ok, so you might not be convinced by my post where I try and convince you that $1 = 0.9...$
Let's try another tack.

Using long division we find that $\frac{1}{3}= 0.3...$

Multiplying both sides by 3

$\frac{3}{3}=0.9...$

Simplifying

$1=0.9...$

QED