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Rounding rules
Beginner
Results should not be reported with more precision than the inputs.
In multiplication and division, round the result to the fewest significant figures of any input. In addition and subtraction, round to the fewest decimal places. Keep an extra digit in intermediate steps and round only at the end.
12.11 + 0.3 = 12.4 (one decimal place). 4.56 × 1.4 = 6.4 (two sig figs).
Rounding early and repeatedly compounds small errors and can shift the final digit.
In more detail
When rounding, look at the first digit you are dropping. Round up if it is 5 or more, and keep the digit as it is if it is 4 or less. Round only at the final step to avoid compounding errors.
Real-world uses
- A calculated area of 12.3456 m² is reported as 12.35 m² when the inputs have four significant figures.
- Financial and engineering spreadsheets are set to round only the displayed result, not the stored value.
- When a lab sheet multiplies a measured length of 2.1 m by a width of 3.456 m, the answer is quoted to two significant figures, which is 7.3 m².
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Frequently asked questions
Should I round intermediate results?
No. Keep extra digits during the calculation and round the final answer, otherwise small errors can add up.
What is round half to even?
It rounds 2.5 to 2 and 3.5 to 4 so that rounding errors cancel on average. Many scientific tools use this rule.
Do I round my final answer only once?
Yes. Keep extra digits during the calculation and round only at the end, otherwise small rounding errors add up.
Related topics in Measurement & Math Tools
Measuring time · Mass vs weight · Significant figures · Accuracy vs precision · Systematic error · Random error