Simplify the following:
$$\frac{{{{\left( {0.1} \right)}^2} + {{\left( {0.01} \right)}^2} + {{\left( {0.009} \right)}^2} + 2\left[ {0.1 \times 0.01 + 0.01 \times 0.009 + 0.009 \times 0.1} \right]}}{{0.01 + 0.001 + 0.0009}}$$

Solution (By Examveda Team)

$$\eqalign{ & \frac{{{{\left( {0.1} \right)}^2} + {{\left( {0.01} \right)}^2} + {{\left( {0.009} \right)}^2} + 2\left[ {0.1 \times 0.01 + 0.01 \times 0.009 + 0.009 \times 0.1} \right]}}{{0.01 + 0.001 + 0.0009}} \cr & = \frac{{10{{\left( {0.1 + 0.01 + 0.009} \right)}^2}}}{{\left( {0.1 + 0.01 + 0.009} \right)}} \cr & = 10 \times 0.119 \cr & = 1.19{\text{ Answer}} \cr} $$