Find the value of the expression given below, correct upto 2 decimal places.

\(\frac{(0.96)^{3}-(0.1)^{3}}{(0.96)^{2}+0.096+(0.1)^{2}}\)

Given:

The value of \(\frac{{{{\left( {0.96} \right)}^3} - {{\left( {0.1} \right)}^3}}}{{{{\left( {0.96} \right)}^2} + 0.096 + {{\left( {0.1} \right)}^2}}}{\rm{ }}\)

Formula Used:

\(\frac{a^3 - b^3}{a^2 + ab + b^2} = a - b\)

Calculation:

Here, a = 0.96 and b = 0.1 .

Using the formula:

\(\frac{{(0.96)^3 - (0.1)^3}}{{(0.96)^2 + (0.96 \times 0.1) + (0.1)^2}}\)

⇒ \(\frac{{(0.96)^3 - (0.1)^3}}{{(0.96)^2 + 0.096 + (0.1)^2}}\)

⇒ 0.96 - 0.1

⇒ 0.86

The correct answer is option 3.