The value of $\frac{(0.013)^3 + (0.007)(0.000049)}{(0.007)^2 + 0.013(0.013 - 0.007)}$ is _____.

0.02

$\frac{(0.013)^3 + (0.007)(0.000049)}{(0.007)^2 + 0.013(0.013 - 0.007)}$

Neglect all the places of decimal because all the numbers having the same place after the decimal.

So the equation can be written as,

$\frac{(13)^3 + (7^3)}{(7)^2 + (13)^2 (7 \times 13)}$

a³ + b³ = ( a + b ) ( a² + b² - ab )

= \(\frac{(7 + 13)(7^2 + 13^2 - 7 \times 13}{7^2 + 13^2 - 7 \times 13 \times 1000}\)

= \(\frac{20}{1000}\)

= 0.02