Question

Add 0.3333...+0.999...

Answer 1

let
$x = 0.33333... \\ 10x = 3.3333... \\ 10x - x = 3.3333... - 0.3333... \\ 9x = 3 \\ x = \frac{3}{9} \\ x = \frac{1}{3} \\ x = 0.9999...\\ 10x = 9.999... \\ 10x - x = 9.999... - 0.999... \\ 9x = 9 \\ x = 1 \\ add \: both \: of \: them \\ \frac{1}{3} + 1 \\ \frac{1 + 3}{3} \\ = \frac{4}{3} = 1.333333333... \\ = 1.3 \: bar$