Experimental Uncertainty and Error

Also, using the same number of significant figures for both the measurement and the error is not necessary. You can also write it as 670(70) nm or 670(70)x10^-3 mm. It all depends on the level of precision and accuracy that is required for your data.
  • #1
jenny777
28
0
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
 
Physics news on Phys.org
  • #3
jenny777 said:
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).
 
  • Like
Likes 1 person
  • #4
jenny777 said:
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
 
  • Like
Likes 1 person
  • #5
dauto said:
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
 
  • #6
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
 
  • #7
jenny777 said:
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.
 
Last edited:
  • Like
Likes 1 person

Related to Experimental Uncertainty and Error

What is experimental uncertainty?

Experimental uncertainty refers to the potential variability or lack of precision in the measurements or data collected during an experiment. It can arise from various sources such as equipment limitations, human error, or environmental factors.

What is the difference between uncertainty and error?

Uncertainty refers to the potential range of values that a measurement or data point may fall within, while error refers to the difference between the measured value and the true value. Uncertainty is a measure of the precision of a measurement, while error is a measure of accuracy.

How is experimental uncertainty and error calculated?

Experimental uncertainty and error can be calculated using statistical methods such as standard deviation, which measures the spread of data around the mean value. Other measures such as confidence intervals and error bars can also be used to quantify uncertainty and error.

How can experimental uncertainty and error be reduced?

Experimental uncertainty and error can be reduced by using more precise and accurate equipment, carefully controlling experimental conditions, and repeating measurements multiple times. Statistical analysis can also help identify and minimize sources of error.

Why is it important to account for experimental uncertainty and error?

Accounting for experimental uncertainty and error is important because it allows for a more accurate interpretation of experimental results. It also helps to identify potential flaws or limitations in the experimental setup and can guide improvements for future experiments.

Similar threads

Replies
7
Views
706
  • Other Physics Topics
Replies
6
Views
2K
Replies
1
Views
3K
Replies
1
Views
694
  • Other Physics Topics
Replies
1
Views
3K
  • Other Physics Topics
Replies
13
Views
3K
Replies
1
Views
1K
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
479
  • Other Physics Topics
Replies
4
Views
3K
Back
Top