x=.9999… 10x=9.9999… Subtract x from both sides 9x=9 x=1

There it is, folks.

Somehow I have the feeling that this is not going to convince people who think that 0.9999… /= 1, but only make them madder.

Personally I like to point to the difference, or rather non-difference, between 0.333… and ⅓, then ask them what multiplying each by 3 is.