What is the value of 0.4 ̅ + 0.2 ̅ ?

Correct option is C

Given:
Value to calculate: 0.4̅ + 0.2̅
Here, 0.4̅ means 0.4444... (repeating), and 0.2̅ means 0.2222... (repeating)
Solution:
Let x = 0.4̅ = 0.4444.......(1)

Then,10x = 4.444...(2)
 Subtracting these equations, get

​$$9x = 4 \Rightarrow x = \frac{4}{9} .$$​​
Similarly,0.2̅ = $$\frac{2}{9}$$​ .
0.4̅ + 0.2̅ = $$\frac{4}{9} + \frac{2}{9}$$= $$\frac{4 + 2}{9} = \frac{6}{9}$$​​
​$$\frac{6}{9} = \frac{2}{3}$$​​
Thus, the value of 0.4̅ + 0.2̅ is $$\frac{2}{3} .$$​​