Explanation:
Given, \(x = \left[ {\frac{{{a^2}{b^2}}}{c}} \right],\)
Maximum fractional error in \(x\),
\(\frac{{\Delta x}}{x} = 2\frac{{\Delta a}}{a} + 2\frac{{\Delta b}}{b} + \frac{{\Delta c}}{c}\)
Percentage error is
\( \Rightarrow \left( {\frac{{\Delta x}}{x} \times 100} \right)\)
\( = 2\left( {\frac{{\Delta a}}{a} \times 100} \right) + 2\left( {\frac{{\Delta b}}{b} \times 100} \right) + \left( {\frac{{\Delta c}}{c} \times 100} \right)\)
Here, percentage error in \(a = 2,\)
percentage error in \(b = 3,\)
percentage error in \(c = 4.\)
\(\therefore \,\left( {\frac{{\Delta x}}{x} \times 100} \right) = \,\,(2 \times 2)\, + \,\,(2 \times 3)\, + \,4\, = 14\% \)