Uncertainty??? help

[probablygonnafail]

If you subtract two values that have uncertainty do you add the uncertainty? Do you use absolute uncertainty and then turn it into relative uncertainty somehow or can you use the relative uncertainty?  

I am doing an assignment on isotonic points for vegetables. I have found percentage change for mass and have uncertainty for initial and final mass and I need to be able to say something like for the found isotonic point relative uncertainty for initial is -+20% and for final it is -+24% therefore the uncertainty for the isotonic point is ____.

Not sure if that makes sense but I tried. 

[Country Boy]

Suppose you are given value A with "uncertainty" x%.  That means the true value can be any where from (1- 0.ox)A to (1+ 0.0x)A.  Similarly given value B with "uncertainty" y% means that the true value can be anywhere from (1- 0.0y)B to (1+ 0.0y)B.  The sum of the two can then be any where from (adding the two lowest possible values) (1- 0.0x)A+ (1- 0.0y)B= (A+ B)- 0.0xA- 0.0yB to (adding the largest possible values) (1+ 0.0x)A+ (1+ 0.0y)B= (A+ B)+ 0.0xA+ 0.0yB-  The two "uncertainties" add.  

There is an engineer's "rule of thumb" that "when quantities add their absolute uncertainties add.  When quantities are multiplied, their "relative uncertainties" (percentage uncertainties) add".  The latter is not exact- it ignores the interaction of the  of the uncertainties.  For example, suppose A has a measured value of 200 with a 10%  relative uncertainty so absolute uncertainty of 20.  The actual value can be anywhere from 200- 20= 180 to 200+ 20= 220.   Suppose B has a measured value of 100 with a 5% uncertainty so absolute uncertainty of 5.  The actual value can be anywhere from 100- 5= 95 to 100+ 5= 105.  The A+ B has a calculated value of 200+ 100= 300 but can be any where from 180+ 95= 275 to 220+ 105= 325.  That is, [tex]A+ B= 300\pm 25[/tex].  The absolute uncertainty is 25= 20+ 5, the sum of the two absolute uncertainties.

 

[probablygonnafail]

Thank you so much!! 

 

[John Cuthber]

It rather depends how you calculate the error margins.

If you express them as standard deviations then you add variances rather than adding absolute error margins.