Lab report help: calculating uncertainty

[theIBnerd]

Homework Statement

I have a problem while writing the uncertainty of datas in my lab report (portfolio).
So, here is my question:

While multiplying some data with different uncertainties, I do multiply their uncertainties too, right?

Then, if the multiplication of uncertainities has less digits after comma than that of the actual multiplication af data; should I round up some digits of the actual multiplication of data?

Homework Equations

To make it more clear, here is an example:

Work= Force x distance
W(J)= m(kg) ±0.1 kg x g(m/sec2) ±0.1 m/sec2 x h(m) ±0.01 m
W= 47.9 kg x 9.79 m/sec2 x 3.975 m
W= 1864.040475 kg x m2/sec2= 1864.040475 Joule ±0.0001 Joule

The Attempt at a Solution

Should it be like:
W= 1864.0405 Joule ±0.0001 Joule ?

 

[hotcommodity]

When multiplying terms with calculated uncertainties, you cannot multiply the uncertainties themselves. Unless you're given an error equation, one of the best ways to go about finding the uncertainty for a quantity (such as work) is to use the computational method.

If you're trying to calculate work for example, and you have uncertainties in force and distance, you want to find the uncertainty in the work caused by the uncertainty in the force $$\delta_{W,F}$$, as well as the uncertainty in the work cause by the uncertainty in the distance $$\delta_{W,d}.$$. Once you obtain these quantities, you can square them, add them together and take the square root to obtain the uncertainty in the work. It would be a little lengthy to describe the entire computational method, so I would suggest researching it online. I hope that helps.

 

[theIBnerd]

First of all, thanks a lot! It really helped. My physics teacher does not give us these "details" (which I don't think so); I believe he expects us to suddenly come up with the idea of this process for uncertainties. Thank you anyway.