Find the value of $$\frac{{(0.01)^2 + (0.22)^2 + (0.333)^2 + (0.4444)^2 + (0.55555)^2}}{{(0.001)^2 + (0.022)^2 + (0.0333)^2 + (0.04444)^2 + (0.055555)^2}}$$​​

Correct option is B

Given:

​$$\frac{{(0.01)^2 + (0.22)^2 + (0.333)^2 + (0.4444)^2 + (0.55555)^2}}{{(0.001)^2 + (0.022)^2 + (0.0333)^2 + (0.04444)^2 + (0.055555)^2}}$$ 

Solution:

​$$\frac{{(0.01)^2 + (0.22)^2 + (0.333)^2 + (0.4444)^2 + (0.55555)^2}}{{(0.001)^2 + (0.022)^2 + (0.0333)^2 + (0.04444)^2 + (0.055555)^2}}$$ 

​To make the two terms comparable, we can multiply both the numerator and the denominator by $100$:

= $$\frac{100\times[{{(0.01)^2 + (0.22)^2 + (0.333)^2 + (0.4444)^2 + (0.55555)^2}}]}{100\times[{{(0.001)^2 + (0.022)^2 + (0.0333)^2 + (0.04444)^2 + (0.055555)^2}}]}$$ 

 = $$\frac{100\times[{{(0.01)^2 + (0.22)^2 + (0.333)^2 + (0.4444)^2 + (0.55555)^2}}]}{[{(0.01)^2 + (0.22)^2 + (0.333)^2 + (0.4444)^2 + (0.55555)^2}]}$$ 

= 100 

the value of the expression is 100.