Please, consult your scientific calculator's, and perform the following keystrokes:

(1/3)= <-- This result should display 0.33333333333333333

(([result])*3)= <-- This result should equal 1.

Then, perform the following:

(1/3)=

(([result])+(1/3))= <-- This result should display 0.6666666666666666

(([result])+(1/3))= <-- This result should equal 1.

If you performed this, you just proved that .999999999...=1

So, knowing that (1/3)=0.3333333333333..., then it is easy to conclude that(0.3333333333...)*3 = (0.999999999999...) = 1, which is the same as (0.3333333333...) + (0.3333333333...) + (0.3333333333...) = (0.999999999999...) = 1.