Add, subtract, multiply and divide uncertainties in measurement.

[Sassenav22]

Can someone show me how to add, subtract, multiply and divide uncertainties in measurement.

 

[LCKurtz]

I'm not sure I understand your question. Do you mean something like given errors in measuring a and b estimate the error in calculating some function f(a,b)? Or something else?

 

[Sassenav22]

errors in measurement like 0.06 plus and minus 5% and 0.09 plus and minus 3%

 

[Gerenuk]

Maybe
http://en.wikipedia.org/wiki/Propagation_of_uncertainty
makes sense to you. Especially the examples.
For uncorrelated variables the covariances and the correlation factor are zero.

 

[CellCoree]

I can provide you with the necessary steps to add, subtract, multiply, and divide uncertainties in measurement.

1. Adding uncertainties: When adding two or more quantities with uncertainties, the uncertainties must be added together to find the total uncertainty. For example, if we have two measurements, A = 10 ± 0.5 and B = 15 ± 0.7, the total uncertainty when adding them together would be 0.5 + 0.7 = 1.2. Therefore, the final result would be A + B = 25 ± 1.2.

2. Subtracting uncertainties: Similar to adding uncertainties, when subtracting two or more quantities with uncertainties, the uncertainties must be subtracted to find the total uncertainty. For example, if we have two measurements, A = 10 ± 0.5 and B = 15 ± 0.7, the total uncertainty when subtracting them would be 0.5 + 0.7 = 1.2. Therefore, the final result would be A - B = -5 ± 1.2.

3. Multiplying uncertainties: When multiplying two or more quantities with uncertainties, the relative uncertainties must be multiplied to find the total relative uncertainty. For example, if we have two measurements, A = 10 ± 0.5 and B = 15 ± 0.7, the relative uncertainties would be 0.5/10 = 0.05 and 0.7/15 = 0.0467. Multiplying these relative uncertainties gives us the total relative uncertainty of A x B = 10 x 15 ± (0.05 x 0.0467) = 150 ± 0.02335.

4. Dividing uncertainties: Similar to multiplying uncertainties, when dividing two or more quantities with uncertainties, the relative uncertainties must be divided to find the total relative uncertainty. For example, if we have two measurements, A = 10 ± 0.5 and B = 15 ± 0.7, the relative uncertainties would be 0.5/10 = 0.05 and 0.7/15 = 0.0467. Dividing these relative uncertainties gives us the total relative uncertainty of A/B = 10/15 ± (0.05/0.0467) = 0.667 ± 0.00107.

It is important to note that uncertainties