What is the formula for error analysis in multiplication and division?

[zak8000]

Homework Statement

hi there i am currently working on a lab report which involves intense error anaylsis and i stink at it so i have made up the following two questions to understand how to perform error analysis with multiplication and division

if x=3+-2 m y=5+-3 s

then what is x*y answer in the form a+-b where a is the mean and b is the error

and also what is x/y in the form a+-b where a is the mean and b is the error

please help!

Homework Equations

The Attempt at a Solution

 

[NuclearNut]

Hi, the basic rules for error analysis are that for addition and subtraction working with absoulte errors ie plus or minus 1cm would be an example of an absolute error, you just add or subtract the values, and the new error in both cases is given by the square root of the sum of the squares of the absoute errors. ie sqrt[(error in a)^2 + (error in b)^2]



For multiplication or division, you just multiply or divide the values and the new error is given by the same formula but instead of using absolute errors, use relative errors, ie percentage errors, so depending on what sort of errors you have to start with you may just have a bit of switching between absolute and relative errors where

relative error = (absolute error)/value

so considering the values you gave

x*y = 3*5 +- sqrt[(2/3)^2+(3/5)^2)*3*5 = 15+-sqrt(181/225)*15 = 15 +-13.45

and x/y= 3/5 +- sqrt[(2/3)^2+(3/5)^2)*3/5 = 0.6 +- 0.538

Hope this helps