Percentage error and significant figure

In summary, when converting a quoted diameter to a percentage error, the decimal place in which the uncertainty manifests is important. The accuracy of the percentage error can vary within a range, and the uncertainty in the uncertainty is not constrained by the original uncertainty. To retain the same level of guarantee in the original data, the percentage error should be rounded up to the nearest significant figure.
  • #1
mrcotton
120
0

Homework Statement



If a diameter of 15.5 +/- 0.1mm has been quoted and you need to turn this to a percentage error
you get (0.1/15.5)*100 = 0.645...

so you would quote this as a percentage error of 0.6%

If it was 15.3 +/- 0.1mm and again you wanted percentage error
(0.1/15.3)*100 = 0.653...

So you would quote as 0.7%

So this is not to do with significant figures but the decimal place in which the uncertainty manifests?

I would be grateful if someone could tell me if this logic is correct

Thanks
 
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  • #2
The accuracy of "0.6%" is just "something between 0.55% and 0.65%", so steps of 0.1% can happen. The figure is right ("significant") in both cases.
As intermediate result, I would probably give 0.65% as uncertainty in both cases.
 
  • #3
The uncertainty in the uncertainty is not constrained by the original uncertainty. If you are quite certain that the error in the 15.5 number is no more than +/-.1, you can quote that as a percentage with as many digits as you like. But if you want to retain the level of guarantee in the original data, you must round it up, not to the nearest. E.g. .65%, .66% respectively.
 

FAQ: Percentage error and significant figure

What is percentage error and how is it calculated?

Percentage error is a measure of the inaccuracy of a measurement or calculation. It is calculated by taking the absolute value of the difference between the measured or calculated value and the actual or accepted value, divided by the actual value, and multiplied by 100 to convert to a percentage.

What are significant figures and why are they important?

Significant figures, also known as significant digits, are the digits in a number that carry meaning or contribute to the precision of a measurement or calculation. They are important because they help to indicate the level of uncertainty in a measurement or calculation, and they also ensure that calculations are carried out with the appropriate level of precision.

How do you determine the number of significant figures in a measurement or calculation?

In a measurement, all non-zero digits, all zeros between non-zero digits, and all final zeros after a decimal point are significant. In a calculation, the result should have the same number of significant figures as the number with the fewest significant figures involved in the calculation.

What is the difference between absolute error and relative error?

Absolute error is the absolute value of the difference between the measured or calculated value and the actual or accepted value, while relative error is the absolute error divided by the actual value. Relative error is usually expressed as a percentage and allows for comparison between different measurements or calculations, while absolute error gives a more direct measure of the difference between values.

How can you minimize percentage error and increase the number of significant figures in a measurement or calculation?

To minimize percentage error, you can improve the precision of the measurement by using more accurate instruments or techniques. To increase the number of significant figures, you can use a measuring device with more decimal places, or use a more precise calculation method that takes into account more significant figures in the input values.

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