A physical quantity a is related to four observable x y z and m as fol

1.	A physical quantity a is related to four observable x y z and m as follows A equal to xy/mz the percentage errors of measures in x y z and m are 4 % 3% 2% and 1% respectively what is the percentage error in the quantity A
Answer» Answer: Given: A RELATIONSHIP has been provided as follows : $\boxed{ \huge{ \sf{a = \dfrac{xy}{mz}}}}$ To find: Max error in "a" when error of each quantity has been given. Concept: Max error can be found by adding the error of each quantity MULTIPLIED with the respective exponential in the given Equation. Calculation: $\boxed{ \sf{ \red{ \frac{ \Delta a}{a} = \dfrac{ \Delta x}{x} + \dfrac{ \Delta y}{y} + \dfrac{ \Delta m}{m} + \dfrac{ \Delta z}{z}}}}$ $\sf{ \implies \dfrac{ \Delta a}{a} = 4 + 3 + <klux>1</klux> + 2}$ $\sf{ \implies \dfrac{ \Delta a}{a} = 10\%}$ So final answer : $\boxed{ \sf{max \: error = 10\%}}$ Additional information: For max error , always ADD the individual errors. Remember to MULTIPLY each term with exponential (here exponential was 1) Express the final answer in percentage.

A physical quantity a is related to four observable x y z and m as follows A equal to xy/mz the percentage errors of measures in x y z and m are 4 % 3% 2% and 1% respectively what is the percentage error in the quantity A

Answer»

A RELATIONSHIP has been provided as follows :

$\boxed{ \huge{ \sf{a = \dfrac{xy}{mz}}}}$

Max error in "a" when error of each quantity has been given.

Max error can be found by adding the error of each quantity MULTIPLIED with the respective exponential in the given Equation.

$\boxed{ \sf{ \red{ \frac{ \Delta a}{a} = \dfrac{ \Delta x}{x} + \dfrac{ \Delta y}{y} + \dfrac{ \Delta m}{m} + \dfrac{ \Delta z}{z}}}}$

$\sf{ \implies \dfrac{ \Delta a}{a} = 4 + 3 + <klux>1</klux> + 2}$

$\sf{ \implies \dfrac{ \Delta a}{a} = 10\%}$

So final answer :

$\boxed{ \sf{max \: error = 10\%}}$