question_answer

A physical quantity \[x=\frac{{{a}^{2}}{{b}^{-3/2}}}{{{c}^{4}}}\]has a relative error\[\frac{\Delta x}{x}=2\frac{\Delta a}{a}-\frac{3}{2}\frac{\Delta b}{b}-4\frac{\Delta c}{c}\].Is the statement correct?             

Answer:

                No, as combined error is additive only without algebraic sign. The correct statement is \[\frac{\Delta x}{x}=2\frac{\Delta a}{a}+\frac{3}{2}\frac{\Delta b}{b}+4\frac{\Delta c}{c}\]