Simplify the following:

$$\frac{(0.002)^2 + (0.033)^2 + (0.0444)^2 + (0.05555)^2}{(0.02)^2 + (0.33)^2 + (0.444)^2 + (0.5555)^2}$$​​

Correct option is A

Given:

$$\frac{(0.002)^2 + (0.033)^2 + (0.0444)^2 + (0.05555)^2}{(0.02)^2 + (0.33)^2 + (0.444)^2 + (0.5555)^2}$$

Solution:

​$$\frac{(0.002)^2 + (0.033)^2 + (0.0444)^2 + (0.05555)^2}{(0.02)^2 + (0.33)^2 + (0.444)^2 + (0.5555)^2}$$

Common $$\frac{1}{10^2}$$ in numerator:

= $$\frac{\frac{1}{10^2}[(0.02)^2 + (0.33)^2 + (0.444)^2 + (0.5555)^2]}{(0.02)^2 + (0.33)^2 + (0.444)^2 + (0.5555)^2}$$

= $$\frac{1}{10^2}$$

= $$\frac{1}{100}$$

= 0.01

Thus, the correct answer is (a).