I was prepared to blow my then 6th or 7th grade daughter's mind with this algebraic proof. I started by asking if 0.999... = 1, to which she said "no." I rephrased it and said it is equal, do you know why? She thought for a moment and said "1/9 is 0.111..., so 9/9 is 0.999... and 9/9 is 1." And I had to admit she had a far better solution than I did.

Because I wondered, it’s not a trick:

x = 0.444444...

10x = 4.444444...

10x - x = 4

9x = 4

x = 4/9 = 0.444444...

All the single digit repeating decimals are x/9.

0.111... == 1/9

0.222... == 2/9

...

0.888... == 8/9

0.999... == 9/9 :)

That's how I was taught in my Algebra class

black magic! I wonder if there are any programming languages that are able to handle this properly?

https://www.wolframalpha.com/input/?i=10*0.9...-0.9...

There are programming languages with rational number types, but none that I know of that represent numbers as repeating decimals.