Question

prove 1=0.9999... help

Answer 1

Let x = 0.9999....
10 x = 9.9999....
So, 10x - x = 9.9999...-0.9999...
=> 9x = 9
=> x = 9/9
=> x = 1 ( Hence proved)

Answer 2

Yo!
Your Answer.

To prove : 1 = 0.9999.. ____[y]

Proof:
Let x = 0.9999... ____________(1.)

Multiply bother sides by 10

10 x = 9.9999... _____________(2.)

Sub. eq(1.) from eq(2.)

10x = 9.9999 - 0.9999

9x = 9

x = 9/9

x = 1 _____[z]

Comparing eq[y] and [z]

1 = 0.9999......

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~{'Hence\: proved'}$