Why is uncertainty written as ±1 in the last digit?

The uncertainty is often given as plus or minus one in the last digit because it reflects the typical range of error when estimating that final digit between scale marks.

When you read a measurement like three point four five centimeters and the uncertainty is plus or minus one in the last digit, that means the true value is expected to be within one unit of the smallest recorded digit, so three point four four to three point four six centimeters if the last digit is five. Think of a ruler with tiny marks that are too small to read perfectly; you make your best guess for the last number and that guess could easily be one tick higher or lower. This convention is a simple way to show that the final digit is uncertain without writing a complicated error analysis, and it matches how most people estimate when they cannot read between the marks exactly. It is a practical shorthand used in labs and reports to communicate that the limit of precision is at the last digit recorded.

Students commonly forget to treat the last digit as an estimate and report too many digits, which makes the measurement seem falsely precise; the fix is to round reported values so that the uncertainty applies to the last shown digit. Another mistake is writing an uncertainty with more significant figures than the measurement; always give the uncertainty with one digit in the last place and match the measurement to that precision. Some people misunderstand plus or minus one as a fixed rule rather than a convention tied to how the measurement was made, so remember to increase your uncertainty if your measuring method was rougher than estimating between marks.

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Why Uncertainty Is Given as ±1 in Last Digit

1. Last digit indicates precision
2. True value within one unit
3. Estimate between scale marks
4. Guess could be one tick off
5. Use convention to show uncertainty
6. Match uncertainty to measurement method

Common Measurement Mistakes with Uncertainty

1. Reporting too many digits
2. Giving uncertainty with extra figures
3. Treating ±1 as absolute rule

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