Experimental Uncertainty and Error

[jenny777]

Hello all,

I used the micrometer in my lab that has a resolution of 100 nm.
so, my measurement looks something like,

0.2345 mm, with an uncertainty of 0.00005 mm.

But I don't want to write, (0.2345 +/- 0.00005)mm in my data table because it just looks a little awkward to have so many zeros inside my table.

Is there a better way of writing the measurement above? (with it's uncertainty)?

Also, I noticed that there are 2 types of error. One is standard error and then the second one being resolution error.

How can I combine the two? so will my resolution error be 50 nm ? I'm subtracting the two measurements to yield delta d, so will my reading error be, sqrt (50^2+50^2)≈71 nm ?

Thank you

 

[UltrafastPED]

Here is a standard lab writeup: http://physicsed.buffalostate.edu/pubs/MeasurementAnalysis/MA1_9ed.pdf

Here is a more concise notation, courtesy of NIST:
http://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html

And rules for combining uncertainties: http://physics.nist.gov/cuu/Uncertainty/index.html

 

[Simon Bridge]

Hello all,

I used the micrometer in my lab that has a resolution of 100 nm.
so, my measurement looks something like,

0.2345 mm, with an uncertainty of 0.00005 mm.

But I don't want to write, (0.2345 +/- 0.00005)mm in my data table because it just looks a little awkward to have so many zeros inside my table.

(0.2345 +/- 0.00005)mm = (234.5 $\small{\pm}$0.05)μm = (234.5 $\small{\pm}$0.05)x10^-3mm

better? You can put the 10^-3 or the units at the top of the column in the table (as part of the header).

 

[dauto]

Hello all,

I used the micrometer in my lab that has a resolution of 100 nm.
so, my measurement looks something like,

0.2345 mm, with an uncertainty of 0.00005 mm.

But I don't want to write, (0.2345 +/- 0.00005)mm in my data table because it just looks a little awkward to have so many zeros inside my table.

Is there a better way of writing the measurement above? (with it's uncertainty)?

Also, I noticed that there are 2 types of error. One is standard error and then the second one being resolution error.

How can I combine the two? so will my resolution error be 50 nm ? I'm subtracting the two measurements to yield delta d, so will my reading error be, sqrt (50^2+50^2)≈71 nm ?

Thank you

Use the standard concise notation 0.23450(5) mm where the number in parenthesis is the uncertainty of the last digit of the previous quantity

 

[jenny777]

Use the standard concise notation 0.23450(5) mm where the number in parenthesis is the uncertainty of the last digit of the previous quantity

Shouldn't it be 0.2345(5) mm?
And if I want to write, 666.66 nm +/- 71 nm, how can I represent the uncertainty in parenthesis?

Thank you

 

[GlenS]

Shouldn't it be 0.2345(5) mm?

No, 0.2345(5) indicates a range from 0.2346 to 0.2344. The actual range is 0.23455 to 0.23445

 

[dauto]

Shouldn't it be 0.2345(5) mm?
And if I want to write, 666.66 nm +/- 71 nm, how can I represent the uncertainty in parenthesis?

Thank you

No, 0.2345(5) mm represents (0.2345 +/- 0.0005)mm. You want 0.23450(5) mm which represents (0.2345 +/- 0.00005)mm. Note the extra zero. The number in parenthesis is not an extra digit. It is the uncertainty of the previous digit(s).

666.66(7100) nm = 666.66 nm +/- 71 nm

I would round it to the more practical 667(71) nm. There is no point in using more than 2 significant figures for the error.