# Experimental Uncertainty and Error

1. Mar 26, 2014

### 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

2. Mar 26, 2014

### UltrafastPED

3. Mar 26, 2014

### Simon Bridge

(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).

4. Mar 26, 2014

### dauto

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

5. Mar 26, 2014

### jenny777

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

6. Mar 26, 2014

### GlenS

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

7. Mar 26, 2014

### dauto

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.

Last edited: Mar 26, 2014