# Why are the last two digits of the mass of an electron in parentheses?

• Mason Smith
In summary, the mass of an electron is approximately 0.510 998 9461 MeV/c2, with the last two digits in parenthesis indicating uncertainty. This notation is commonly used in scientific measurements.
Mason Smith
According to Wikipedia, the mass of an electron is 0.510 998 9461(31) MeV/c2. Why are the last two digits of this number in parenthesis? Is this the same thing as saying (0.510 998 9461 ± 0.000 000 0031) MeV/c2.

Mason Smith said:
± 0.000 000 0031

No, it does not mean that. It means that it is approximately equal to 0.510 998 946131 but the last two decimal places are uncertain.

Use of concise notation (from https://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html)

If, for example, y = 1 234.567 89 U and u(y) = 0.000 11 U, where U is the unit of y, then Y = (1 234.567 89 ± 0.000 11) U. A more concise form of this expression, and one that is in common use, is Y = 1 234.567 89(11) U, where it understood that the number in parentheses is the numerical value of the standard uncertainty referred to the corresponding last digits of the quoted result.

Mason Smith
Lord Jestocost said:
Use of concise notation (from https://physics.nist.gov/cgi-bin/cuu/Info/Constants/definitions.html)

If, for example, y = 1 234.567 89 U and u(y) = 0.000 11 U, where U is the unit of y, then Y = (1 234.567 89 ± 0.000 11) U. A more concise form of this expression, and one that is in common use, is Y = 1 234.567 89(11) U, where it understood that the number in parentheses is the numerical value of the standard uncertainty referred to the corresponding last digits of the quoted result.
This helped a lot. Thank you for the reference.

## 1. What is the purpose of showing error in scientific research?

The purpose of showing error in scientific research is to accurately reflect the limitations and uncertainties of the data and calculations used in the study. It allows for a more comprehensive understanding of the results and helps to avoid drawing incorrect conclusions.

## 2. How can error be quantified and expressed in scientific research?

Error can be quantified and expressed in scientific research through various methods such as standard deviation, confidence intervals, and percentage error. These measures provide a numerical value that represents the degree of uncertainty in the data.

## 3. Can error ever be completely eliminated in scientific research?

No, error cannot be completely eliminated in scientific research. There will always be some degree of uncertainty in data and calculations, and it is important to acknowledge and account for this in order to ensure accurate and valid results.

## 4. Why is it important to consider error in scientific research?

Considering error in scientific research is important because it allows for a more accurate and transparent representation of the data and results. It also helps to identify areas of improvement and potential sources of bias or inaccuracy.

## 5. How can error impact the interpretation of scientific findings?

Error can greatly impact the interpretation of scientific findings if it is not properly addressed. Failing to consider error can lead to incorrect conclusions or overgeneralization of results. It is important to understand and communicate the potential sources and implications of error in order to accurately interpret findings.

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