Arithmetic rule
For addition and subtraction, decimal-place precision controls the final answer.
Use the calculatorFor addition and subtraction, the final answer is rounded to the least precise decimal place among the measured inputs. This rule is about place value, not the total number of significant figures.
The raw result is 12.503. Since 12.5 is precise only to tenths, the final answer is 12.5.
The tenths place controls the result because it is the least precise decimal place in the measured inputs.
Look at each measured value before doing the final rounding. Identify the last reliable decimal place for each input, then use the least precise place for the final answer.
2.34 is precise to hundredths, while 1.2 is precise to tenths. The raw sum 3.54 is reported as 3.5.
The raw result is 103.15. Because 105.6 is precise to tenths, report 103.2.
A value can have many significant figures but still control the answer by decimal place. That is why addition and subtraction are different from multiplication and division.
Fewest significant figures controls multiplication and division, not addition and subtraction.
12.5 has 3 significant figures, but it still controls 12.5 + 0.003 because it only reaches the tenths place.
When solving by hand, line up decimal points so the place values are visible. This makes it easier to see which input has the least precise decimal place.
Write the raw arithmetic first, keep guard digits while calculating, then round only the final result.
Subtraction uses the same decimal-place rule as addition. The final result should not claim more decimal precision than the least precise measured value supports.
The raw result is 19.887. Since 20.00 is precise to hundredths, report 19.89.
In lab work, the unit is part of the reported result. Round the number according to the decimal-place rule, then keep the correct unit with the final answer.
Report 12.5 mL because the least precise input is measured to tenths of a milliliter.
Only add or subtract values after the units match. If a problem mixes mL and L, convert first, then apply the decimal-place precision rule.
The biggest mistakes are using the multiplication rule, rounding intermediate values too early, or counting decimal places after the arithmetic instead of before the final rounding choice.
12.5 + 0.003 is reported as 12.5, not because of the fewest-sig-fig rule, but because tenths is the least precise decimal place.
Reporting 12.503 would imply precision to thousandths, which the 12.5 measurement does not support.
A clear report sentence names the rounded value and the decimal-place rule. Keep it short so the reason is easy to check.
The result should be reported as 12.5 because addition and subtraction follow the least precise decimal place.
