​$$\text{The value of } 0.\overline{23} + 0.\overline{22} \text{ is:}$$​​

Correct option is D

Given:

$$0.\overline{23}+0.\overline{22}$$ 

Solution:

​$$0.\overline{23}$$  written as a fraction:

x = $$0.\overline{23}$$ 

100x = $$23.\overline{23}$$ 

​Subtract the original equation from this:

​100x − x = $$23.\overline{23}- 0.\overline{23}$$ 

​99x = 23

x = $$\frac{23}{99}$$ 

​$$0.\overline{22}$$ written as a fraction:

y = $$0.\overline{22}$$ 

100y = $$22.\overline{22}$$ 

​Subtract the original equation from this:

100y - y = $$22.\overline{22} - 0.\overline{22}$$ 

​99y =22 

y = $$\frac{22}{99}$$ 

​$$0.\overline{23}+0.\overline{22}$$ = $$\frac{23}{99}+\frac{22}{99}$$ = $$\frac{45}{99}$$ = $$\frac{5}{11}$$ 

​So, the value of $$0.\overline{23}+0.\overline{22}$$ is $$\frac{5}{11}$$ which is approximately 0.454545....​

Thus, correct answer is (d) 0.454545....