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.

I’d just say that not all fractions can be broken down into a proper decimal for a whole number, just like pie never actually ends. We just stop and say it’s close enough to not be important. Need to know about a circle on your whiteboard? 3.14 is accurate enough. Need the entire observable universe measured to within a single atoms worth of accuracy? It only takes 39 digits after the 3.

pi isn’t even a fraction. like, it’s actually an important thing that it isn’t