# Lab report help: calculating uncertainty

## 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 ?

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.