Question

how do I solve from this? pls don't only give me the answer. step by step pls. Rewrite as a simplified fraction​

Answer 1

Answer:

$\frac{1}{9}$

Step-by-step explanation:

Create 2 equations with the repeating part after the decimal point. Then by subtracting the repeating part is eliminated

let x = 0.1111.... → (1) ← multiply both sides by 10

10x = 1.1111.... → (2)

Subtract (1) from (2) eliminating the repeater, that is

9x = 1 ( divide both sides by 9 )

x = $\frac{1}{9}$

That is

0.111111... = $\frac{1}{9}$