The simplified value of $$\frac{(0.11)^2 + (0.06)^2 + (0.031)^2}{(0.011)^2 + (0.006)^2 + (0.0031)^2}$$​​

Correct option is D

Given:

$$\frac{(0.11)^2 + (0.06)^2 + (0.031)^2}{(0.011)^2 + (0.006)^2 + (0.0031)^2}$$​

Solution:

​$$\frac{(0.11)^2 + (0.06)^2 + (0.031)^2}{(0.011)^2 + (0.006)^2 + (0.0031)^2}$$ 

Multiplying by 100 both the numerator and denominator 

​$$= \frac{100\times[(0.11)^2 + (0.06)^2 + (0.031)^2]}{100\times[(0.011)^2 + (0.006)^2 + (0.0031)^2]}$$ 

​$$= \frac{100\times[(0.11)^2 + (0.06)^2 + (0.031)^2]}{[(0.11)^2 + (0.06)^2 + (0.031)^2]}$$ 

$$=100$$​  

Thus the simplified value of the given expression is 100.

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