Correct way to report significant digits in measurements and their uncertainty (calculating stream density)

[jones123]

Hi,

I am calculating the stream density S (= river length L divided by stream area A). The river has a length L of 671.8 +- 5.9 km and the stream area is 1860.2 +- 19.8 km^2. The stream density is thus and 0.36114396 km^-1 its error (calculated by the laws of error propagation by division) is 0.00498359 km^-1. What is the correct way to report this value and its uncertainty with respect to significant figures and/or digits after the decimal point? And why?

Thanks.

 

[blamocur]

1. https://courses.cit.cornell.edu/virtual_lab/LabZero/Significant_Figures.shtml
2. https://web.ics.purdue.edu/~lewicki/physics218/significant
3. https://en.wikipedia.org/wiki/Significant_figures
4. https://www.math.drexel.edu/~tolya/300_errors.pdf
5. https://www.ruf.rice.edu/~bioslabs/tools/data_analysis/errors_sigfigs.html
6. https://chem.libretexts.org/Bookshe..._their_measurements/1.04:_Significant_Figures

 

[Dr.Peterson]

Hi,

I am calculating the stream density S (= river length L divided by stream area A). The river has a length L of 671.8 +- 5.9 km and the stream area is 1860.2 +- 19.8 km^2. The stream density is thus and 0.36114396 km^-1 its error (calculated by the laws of error propagation by division) is 0.00498359 km^-1. What is the correct way to report this value and its uncertainty with respect to significant figures and/or digits after the decimal point? And why?

Thanks.

It will be helpful if you show us what you think the answer should be, and why you are not so sure of it. It seems straightforward, at least on the surface.

It's worth keeping in mind that significant figures are just a rule of thumb, and are not nearly as precise as the way you indicated accuracy of your data, so there may well be different opinions. (It sounds like you may have more than one opinion yourself.)