5. express 0.2̅ as a fraction in simplest form.

Explanation:

Step1: Let x = 0.222...

$x = 0.222\cdots$

Step2: Multiply both sides by 10

$10x=2.222\cdots$

Step3: Subtract the first - equation from the second - equation

$10x - x=(2.222\cdots)-(0.222\cdots)$ $9x = 2$

Step4: Solve for x

$x=\frac{2}{9}$

Answer:

$\frac{2}{9}$