# How to round off percentage uncertainties?

In summary, when rounding off percentage uncertainties, it is important to follow the rule of using the same number of significant figures as the smallest value given or calculated. In the example given, the error is quoted as +/- 0.5mm, therefore the percentage uncertainty should be rounded off to one significant figure, resulting in 0.2%. Using more significant figures would not be justified in error analysis.
How to round off percentage uncertainties?

Here's is an example question:

Find the percentage of uncertainty in (225.7+/-0.5)mm.
I know that to find out percentage, it's simply 0.5/225.7 x 100 = 0.22153088...%

Now, my question is, how much do I round off for this percentage uncertainty? Should I just round it off to one significant figure? Or Is there a certain rule?

strictly speaking you cannot use more sig figs than the smallest you are given/calculate...that is what the word 'significant' means (If they are not significant then they are insignificant !)
Your error is quoted as +/-0.5mm which means 1 significant figure so I would say round off to 0.2%
I would challenge anyone dealing with error analysis to justify that this should be given to 2 or 3 sig figs.

## 1. How do I round off percentage uncertainties?

To round off percentage uncertainties, you can follow these steps:

• Step 1: Determine the significant figures in the measured value and the uncertainty.
• Step 2: Identify the first non-zero digit in the uncertainty.
• Step 3: If the digit to the right of the first non-zero digit is less than 5, leave the first non-zero digit unchanged and drop all digits to the right. If the digit is 5 or greater, round the first non-zero digit up by 1 and drop all digits to the right.
• Step 4: If the first non-zero digit is the last digit in the uncertainty, round the measured value up or down accordingly.

## 2. Should I round up or down when dealing with percentage uncertainties?

When rounding off percentage uncertainties, you should always round the first non-zero digit in the uncertainty up if it is 5 or greater, and down if it is less than 5. However, if the first non-zero digit is the last digit in the uncertainty, you should round the measured value up or down accordingly.

## 3. Can I round off percentage uncertainties to a specific number of significant figures?

Yes, you can round off percentage uncertainties to a specific number of significant figures. Simply follow the same steps as mentioned above, but instead of dropping all digits to the right of the first non-zero digit, drop all digits after the desired number of significant figures.

## 4. Is it necessary to round off percentage uncertainties?

Rounding off percentage uncertainties is not always necessary, but it can be helpful in simplifying and communicating the level of uncertainty in a measurement. It is important to follow rounding rules to maintain accuracy and consistency in calculations.

## 5. Are there any exceptions to rounding off percentage uncertainties?

Yes, there are a few exceptions to rounding off percentage uncertainties. For example, when calculating the average of multiple measurements with different uncertainties, it is best to use the unrounded values to maintain accuracy. Additionally, if a calculation involves multiplying or dividing by a number with significant figures, the final result should be rounded off to the same number of significant figures as the number with the least number of significant figures.

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