How Do You Calculate Relative Error in Mass Measurement?

[dewalken]

Assume the density of air was measured as 1.00 kg/m3 ± 5%. The room has dimensions 4 m × 5 m × 2 m, each measured with 10% relative error. What is the mass of the air in the room? What is the relative error for the mass?

I think this is a very simple problem, and i found what the mass of the air would be, i just don't understand relative errors, so how do i find the relative error for the mass?

D = m/V D = 1.00 kg/m3 V = (4 m *5 m *2 m) = 40 m3
m = (1.00 kg/m3)/ (40 m3)
m = .025 kg → m = .03 kg

relative error: Is it something like 5%/ 10% ??

 

[learningphysics]

Have you studied the rule for how to get the relative error when you multiply two quantities?

 

[dewalken]

no, we didn't learn much about relative error at all.

 

[learningphysics]

Have a look at this page:

http://www.rit.edu/~uphysics/uncertainties/Uncertaintiespart2.html

I myself don't know that much about how to treat relative errors... but it seems like when you multiply quantities you add relative errors.

In your calculation there are 4 quantities being multiplied. density, length, width, height... so I'm guessing you just add the relative errors to get the relative error of the mass...