When you calculate with measured values, the answer can’t be more precise than the data that went into it. A calculator happily reports 12.52 × 3.1 = 38.812, but the 3.1 was only measured to two significant figures, so those last digits are noise. The significant-figure rules decide how much of the answer to keep. This calculator applies them for you — the multiplication rule or the addition rule as appropriate — and shows which input limited the result.
How to use the significant figures calculator
- Type the first measurement exactly as recorded, keeping trailing zeros (
2.50, not2.5). Scientific notation such as6.02e23is accepted. - Choose the operation.
- Type the second measurement.
- If one value is a count or a defined constant, mark it as exact so it doesn’t limit the answer.
- Read the rounded answer on the tape, along with the unrounded result and the rule that was applied.
The two rules
Multiplication and division: fewest significant figures
Precision in a product depends on relative uncertainty, which significant figures track.
Addition and subtraction: fewest decimal places
When you add, absolute uncertainties combine, so what matters is the place of the last reliable digit, not how many digits there are. That’s why 1200 + 34.56 rounds to 1,200: if 1200 is only known to the nearest hundred, adding 34.56 can’t make the sum more precise than that.
Worked examples
Multiply: 12.52 (4 s.f.) × 3.1 (2 s.f.) = 38.812 → keep 2 s.f. → 39
Add: 12.52 (hundredths) + 3.1 (tenths) = 15.62 → round to tenths → 15.6
Divide: 2.00 (3 s.f.) ÷ 3.0 (2 s.f.) = 0.6666… → keep 2 s.f. → 0.67
Exact factor: 4.20 g per sample × 12 samples (counted, exact) = 50.4 g → 3 s.f. from 4.20 → 50.4 g
Notice that subtraction can wipe out significant figures: 10.02 − 10.01 = 0.01, which has only one significant figure even though both inputs had four. This loss of precision is why scientists avoid subtracting nearly equal measurements.
Common mistakes
- Using the multiplication rule for addition. 12.52 + 3.1 is not “2 significant figures” (16); it is rounded to the tenths place (15.6).
- Dropping trailing zeros when entering data. A balance reading of 2.50 g has three significant figures. Typing 2.5 throws one away.
- Letting exact numbers limit the answer. Multiplying by 2 to double a recipe, or by 100 to convert meters to centimeters, never reduces the significant figures.
- Rounding at every step. In a chain of calculations, carry a guard digit or two and round once at the end. Rounding repeatedly can shift the final digit.
- Ambiguous whole numbers. 1200 is treated as having two significant figures. If you measured it to the nearest unit, write 1200. or 1.200 × 10³. The significant figures counter shows how any value is read.
Mixed operations
For an expression such as (12.52 + 3.1) × 2.0, apply the rules in the same order you calculate:
- 12.52 + 3.1 = 15.62, good to the tenths place (3 significant figures: 15.6). Keep 15.62 for now.
- 15.62 × 2.0 = 31.24. The factors carry 3 and 2 significant figures, so the answer has 2: 31.
Related tools
To round a single value to a chosen number of significant figures, use the significant figures rounding calculator. For arithmetic with very large or small values written in powers of ten, the scientific notation calculator keeps the exponents straight. Comparing your result with an accepted value? Finish with the percent error calculator.
Frequently asked questions
What are the significant figure rules for multiplication and division?
The answer keeps as many significant figures as the measurement with the fewest. 12.52 × 3.1 = 38.812, but 3.1 has only two significant figures, so the answer is 39.
What are the significant figure rules for addition and subtraction?
The answer is rounded to the last decimal place that every measurement shares — the least precise place. 12.52 + 3.1 = 15.62, but 3.1 is only known to the tenths place, so the answer is 15.6.
How do exact numbers affect significant figures?
They don't limit the answer. Counted values (3 trials, 12 eggs) and defined conversions (1 inch = 2.54 cm exactly) have unlimited significant figures, so only the measured values decide the rounding.
How do I handle a calculation with several steps?
Keep extra digits in the intermediate results and round only the final answer. For mixed operations, track the significant figures or decimal places step by step, applying the rule that matches each operation.
Why did my answer turn into scientific notation?
When the correctly rounded answer ends in zeros that are significant, plain notation would hide them. 2.0 × 50.0 = 100 to two significant figures, which is clearest as 1.0 × 10².