Significant Figures Calculator
Count significant figures digit by digit, round to any number of sig figs, and add, subtract, multiply or divide measurements with the correct sig fig rules, step by step.
How many significant figures a number has, and which digits they are.
Type it as measured, keeping trailing zeros: 0.00450, 1002, 4500, 3.40 × 10^5 or 3.40e5.
- 0: leading zero, not significant
- point: decimal point
- 0: leading zero, not significant
- 0: leading zero, not significant
- 4: non-zero digit, significant
- 5: non-zero digit, significant
- 6: non-zero digit, significant
- 0: trailing zero, significant
- 0: trailing zero, significant
- Non-zero digits are always significant: 4, 5, 6.
- The 3 leading zeros are not significant: they only locate the decimal point.
- The 2 trailing zeros are significant because the number has a decimal point: they were written to show the precision of the measurement.
- Significant digits
- 4 5 6 0 0
- Scientific notation
- 4.5600 × 10⁻³Shows the same number of significant figures unambiguously
- Decimal places
- 7Digits after the decimal point: a different count from significant figures
Rules for significant figures
| Rule | Example | SF |
|---|---|---|
| 1. Non-zero digits are always significant | 345 | 3 |
| 2. Zeros between non-zero digits (captive zeros) are significant | 1002 | 4 |
| 3. Leading zeros are not significant | 0.0045 | 2 |
| 4. Trailing zeros after a decimal point are significant | 4.500 | 4 |
| 5. Trailing zeros in a whole number are ambiguous | 4500 | 2 to 4 |
| 6. In scientific notation, every coefficient digit counts | 4.50 × 10³ | 3 |
Significant figures in calculations
| Operation | Rule | Example |
|---|---|---|
| × and ÷ | Keep the fewest significant figures of any measured value | 2.5 × 3.42 = 8.55 → 8.6 |
| + and − | Keep the least precise decimal place of any measured value | 12.11 + 3.2 = 15.31 → 15.3 |
Round only the final answer; keep every digit in intermediate steps. Exact numbers, such as counts (3 samples) or defined conversions (1 in = 2.54 cm), never limit the result.
All values are handled as exact decimals, so rounding boundaries like 1.005 or 0.15 are decided on the digits you typed, never on binary floating-point approximations. For converting between decimals and powers of ten, see the Scientific Notation Calculator; to round to decimal places instead, use the Rounding Calculator; and for measurement spread, the Standard Deviation Calculator.
Significant figures (sig figs) are the digits in a number that carry real information about how precisely it was measured. This significant figures calculator counts them, shows exactly which digits count and why, rounds any number to the significant figures you need, and applies the sig fig rules to addition, subtraction, multiplication and division.
Type a number exactly as it was written, trailing zeros included: 0.00450 and 0.0045 are different measurements. Decimals, whole numbers, negative values and scientific notation such as 4.56e5 or 4.56 × 10^5 all work. Each answer comes with a digit-by-digit breakdown or step-by-step working, and the arithmetic is exact, so boundary cases like 1.005 round correctly.
Worked Calculation Examples
| Scenario | Result | Calculation Step |
|---|---|---|
| Count: 0.004560 | 4 significant figures | The leading zeros 0.00 only place the decimal point. 4, 5 and 6 are non-zero digits, and the final 0 is a trailing zero after the decimal point, so it is significant: 4, 5, 6, 0. |
| Count: 4500 | 2 to 4 (ambiguous) | The trailing zeros of a whole number without a decimal point may be measured digits or placeholders. Write 4.5 × 10³ (2 SF), 4.50 × 10³ (3 SF) or 4.500 × 10³ (4 SF) to be exact. By contrast, 12345 has no trailing zeros and clearly has 5. |
| Count: 4.500 × 10³ | 4 significant figures | In scientific notation only the coefficient counts: 4.500 has 4 significant figures (its trailing zeros follow a decimal point). The exponent does not count. |
| Add: 12.11 + 3.2 | 15.3 | 12.11 + 3.2 = 15.31. 12.11 is known to the hundredths place but 3.2 only to the tenths, so the answer is rounded to the tenths place: 15.3. |
| Multiply: 2.5 × 3.42 | 8.6 | 2.5 × 3.42 = 8.55. 2.5 has 2 significant figures and 3.42 has 3, so the answer keeps 2: the next digit is 5, so 8.55 rounds up to 8.6. |
| Round: 0.006789 to 3 SF | 0.00679 | Skip the leading zeros and keep 6, 7, 8. The next digit is 9, which is 5 or more, so round 8 up to 9: 0.00679 = 6.79 × 10⁻³. |
| Round with a carry: 9.995 to 3 SF | 10.0 | Keep 9, 9, 9; the next digit is 5, so round up. 999 becomes 1000, which carries into the tens place: 10.0, or 1.00 × 10¹, with 3 significant figures. |
What Are Significant Figures?
Significant figures are the digits in a measured value that convey meaningful precision: every digit that is known reliably, plus the last, estimated one. A length written as 12.30 cm tells you it was measured to the hundredth of a centimeter; written as 12.3 cm, only to the tenth. Both have the same value, but the first carries more information.
Non-zero digits are always significant. Zeros between non-zero digits are significant (1002 has 4). Leading zeros are not: they only place the decimal point, so 0.0045 has 2. Trailing zeros after a decimal point are significant, so 4.500 has 4. Trailing zeros in a whole number without a decimal point, as in 4500, are ambiguous.
Why 0.00450 and 0.0045 Are Different
0.0045 has 2 significant figures and 0.00450 has 3. The extra trailing zero is not decoration: it says the value was measured to the hundred-thousandths place and found to be zero there. Dropping it throws away information about the measurement.
Whole numbers are the tricky case. 1200 could be precise to the hundreds (2 SF), the tens (3 SF) or the ones (4 SF). Scientific notation settles it: 1.2 × 10³ has 2 significant figures, 1.20 × 10³ has 3 and 1.200 × 10³ has 4. Writing a final decimal point, 1200., is another way to show that all four digits are significant.
Significant Figures vs Decimal Places
Significant figures count meaningful digits starting at the first non-zero digit. Decimal places count every digit after the decimal point, zeros included. They measure different things.
0.004560 has 4 significant figures (4, 5, 6 and the final 0) but 6 decimal places. 1234.5 has 5 significant figures but only 1 decimal place. Multiplication and division are governed by significant figures; addition and subtraction by decimal places.
Rounding to Significant Figures
Start at the first non-zero digit and count off the number of significant figures you want. Then look at the first digit you are dropping: if it is less than 5, leave the last kept digit unchanged; if it is 5 or more, round the last kept digit up. Replace dropped digits before the decimal point with zeros so the value keeps its size, and simply drop them after the decimal point.
1.2345 to 3 SF is 1.23, because the next digit is 4. 1.2365 to 3 SF is 1.24, because the next digit is 6. 12,345.678 to 4 SF is 12,350 (1.235 × 10⁴). Rounding can carry: 9.995 to 3 SF is 10.0, where the trailing zero is significant. When a rounded whole number ends in placeholder zeros, scientific notation is the clearest way to show the precision.
Significant Figures in Calculations
Multiplication and division: the answer has as many significant figures as the measured value with the fewest. 2.5 × 3.42 = 8.55, but 2.5 has only 2 significant figures, so the answer is 8.6.
Addition and subtraction: the answer is rounded to the least precise decimal place among the measured values. 12.11 + 3.2 = 15.31, but 3.2 is only known to the tenths place, so the answer is 15.3. Likewise 100.0 + 2.34 = 102.34 rounds to 102.3. Note that the result can have more or fewer significant figures than the inputs: 5.00 − 4.99 = 0.01 has just 1.
Keep all digits during intermediate steps and round only the final answer; rounding at every step lets errors build up.
Exact Numbers vs Measured Numbers
Significant-figure rules describe the precision of measurements. Exact numbers have no measurement uncertainty, so they are treated as having unlimited significant figures and never limit a result. Counted quantities are exact (12 eggs, 3 trials), and so are defined relationships such as 1 inch = 2.54 cm exactly, 1 m = 100 cm or 1 hour = 60 minutes.
So the mass of 3 identical samples of 2.54 g each is 3 × 2.54 = 7.62 g, with 3 significant figures from the measurement, not 1 from the count. Mark such values as exact in the calculator to apply this rule.
Scientific Notation and Significant Figures
In scientific notation, every digit of the coefficient is significant and the exponent does not count. 3.450 × 10⁶ has 4 significant figures, 3.40 × 10⁵ has 3, and 7.20 × 10⁻⁴ has 3. That is why scientific notation is the standard way to report measured values: it states the precision without any ambiguous zeros.
Changing the exponent never changes the count: 4.56 × 10⁵ and 4.56 × 10⁻⁵ both have 3 significant figures. A negative sign doesn't count either; it only shows direction.
Where Significant Figures Matter
Chemistry and physics labs: results computed from measured masses, volumes and times should not claim more precision than the balance, pipette or stopwatch provided. Engineering and manufacturing: tolerances and specifications such as 25.00 mm tell a machinist how precisely a part must be made, and 25 mm would not say the same thing.
Measurement instruments and experimental data: a digital scale reading 0.450 g promises precision to the milligram, while a ruler estimated to 12.3 cm does not support an answer of 12.3456 cm. Significant figures are a compact way of communicating that precision, not just a formatting convention.
How to Use the Significant Figures Calculator
- Choose Count to find how many significant figures a number has, Round to round it to a set number of significant figures, or Calculate to combine two measurements.
- Type the number exactly as it was measured or written, including any trailing zeros: 0.00450 and 0.0045 are different. Scientific notation such as 4.56e5 or 4.56 × 10^5 works too.
- In Count mode, see each digit marked as significant, not significant or ambiguous, with the rule that applies to it.
- In Round mode, enter how many significant figures to keep; the steps show the kept digits, the first dropped digit and whether to round up.
- In Calculate mode, enter both values and choose the operation. Multiplication and division keep the fewest significant figures; addition and subtraction keep the least precise decimal place. Tick “exact” for counted or defined numbers.
Frequently Asked Questions
What are significant figures?
The digits in a measured value that carry meaningful precision: every reliably known digit plus the last, estimated one. 12.30 cm has 4 significant figures and says more about the measurement than 12.3 cm, which has 3.
How do you count significant figures?
Start at the first non-zero digit and count to the last significant digit. Non-zero digits and zeros between them count; leading zeros don’t; trailing zeros count if there is a decimal point and are ambiguous in a whole number without one.
Are leading zeros significant?
No. Leading zeros only place the decimal point, so 0.0045 has 2 significant figures, the same as 4.5 × 10⁻³.
Are trailing zeros significant?
After a decimal point, yes: 4.500 has 4 and 0.00450 has 3. In a whole number without a decimal point, such as 4500, they are ambiguous; use scientific notation or a final decimal point (4500.) to show they are significant.
Are zeros between non-zero digits significant?
Yes. Captive zeros, like the two zeros in 1002 or the zero in 4.05, are always significant.
How do you round to significant figures?
Keep the required number of digits from the first non-zero digit, then look at the next digit: 5 or more rounds the last kept digit up, less than 5 leaves it. 12,345.678 to 4 SF is 12,350, or 1.235 × 10⁴.
What is the difference between significant figures and decimal places?
Significant figures count meaningful digits from the first non-zero digit; decimal places count digits after the decimal point. 0.004560 has 4 significant figures but 6 decimal places.
How many significant figures does 0.00450 have?
Three: 4, 5 and the trailing 0. The leading zeros are not significant, and the trailing zero after the decimal point is.
How many significant figures does 1000 have?
It is ambiguous: anywhere from 1 to 4, depending on whether the zeros were measured. 1 × 10³ has 1, 1.000 × 10³ has 4, and 1000. (with a decimal point) also has 4.
How do you add numbers using significant figures?
Add normally, then round the answer to the least precise decimal place among the measured values. 12.11 + 3.2 = 15.31, rounded to tenths: 15.3. Subtraction works the same way.
How do you multiply numbers using significant figures?
Multiply normally, then round to the fewest significant figures of any measured value. 2.5 × 3.42 = 8.55, and 2.5 has 2 significant figures, so the answer is 8.6.
How do you divide numbers using significant figures?
Divide normally, then round to the fewest significant figures of any measured value, as for multiplication. 4.00 ÷ 3.0 = 1.333…, which rounds to 1.3 because 3.0 has 2 significant figures.
Does scientific notation make significant figures clearer?
Yes. Every digit of the coefficient is significant and the exponent never counts, so 4.50 × 10³ clearly has 3 significant figures, while 4500 could have 2, 3 or 4.
Is zero a significant figure?
It depends on its position. Captive zeros (1002) and trailing zeros after a decimal point (4.50) are significant; leading zeros (0.045) are not; trailing zeros in a whole number (4500) are ambiguous. For a value of zero itself, zeros after the decimal point (0.00) show its precision.
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Last updated: September 27, 2026.