Significant Figures Calculator
Significant figures are the digits in a number that carry real measurement information. This calculator counts the sig figs in any number, rounds to a chosen number of sig figs, and applies the correct rounding rule for calculations, with each step shown.
A sig fig calculator counts the significant figures in any number, rounds a value to a set number of sig figs, and applies the correct rounding rule when you multiply, divide, add, or subtract. Type your number in the tool above, pick what you want to do, and the answer shows with each step. Below you will find instant answers for the numbers people ask about most, worked rounding and calculation examples, and the full rule set with examples you can copy.
How many sig figs in a number? Quick answer
Start counting at the first non-zero digit. Every non-zero digit counts. Zeros trapped between non-zero digits count. Leading zeros never count. Trailing zeros count only when the number has a decimal point. That single rule set decides every case below.
| Number | Sig figs | Reason |
|---|---|---|
| 20.0 | 3 | Decimal point makes the trailing zero count |
| 0.500 | 3 | Leading zero ignored, both trailing zeros count |
| 0.6 | 1 | Only the 6 carries information |
| 0.056 | 2 | Leading zeros never count, 5 and 6 do |
| 6.02 | 3 | Zero sits between two non-zero digits |
| 14.0 | 3 | Trailing zero counts because of the decimal |
| 30.00 | 4 | Decimal makes all trailing zeros count |
| 2.000 | 4 | All three trailing zeros count after the decimal |
| 0.0025 | 2 | Only 2 and 5 count, leading zeros do not |
| 0.150 | 3 | Trailing zero after the decimal counts |
| 100 | 1 | Trailing zeros with no decimal do not count |
| 100.0 | 4 | Decimal makes every zero count |
| 1000 | 1 | No decimal, so only the 1 counts |
| 5000 | 1 | Trailing zeros without a decimal are not significant |
| 45000 | 2 | 4 and 5 count, trailing zeros do not |
| 0.070 | 2 | 7 counts and the final trailing zero counts |
| 500.0 | 4 | The decimal makes all three zeros count |
| 0.01040 | 4 | 1, 0, 4 and the trailing zero count |
| 900 | 1 | No decimal, only the 9 counts |
| 210 | 2 | 2 and 1 count, trailing zero does not |
How many sig figs are in 20.0?
20.0 has 3 significant figures. The 2 counts, the first 0 sits between digits so it counts, and the final 0 after the decimal point counts too. If it were written as 20 with no decimal, it would drop to 1 significant figure, because trailing zeros need a decimal point to count.
How many sig figs are in 0.500?
0.500 has 3 significant figures. The leading zero before the decimal is ignored, it only marks place value. The 5 counts, and both trailing zeros count because they come after the decimal point. Writing 0.500 instead of 0.5 is a deliberate choice that says the value is precise to the thousandths place.
How many sig figs in 0.056, 6.02, 14.0, and 2.000?
These four cover the cases students trip on most:
- 0.056 has 2 sig figs. The two leading zeros only place the decimal. Only 5 and 6 count.
- 6.02 has 3 sig figs. The zero is trapped between 6 and 2, so it counts.
- 14.0 has 3 sig figs. The trailing zero counts because a decimal point is present.
- 2.000 has 4 sig figs. Every trailing zero after the decimal counts, so this is a precise value to the thousandths.
How to count significant figures: the 4 rules
Every result the calculator gives comes from these four rules.
Rule 1: Non-zero digits always count
345 has 3 sig figs. 6.02 has 3. 12.4 has 3. There is no exception here, any digit from 1 to 9 always counts.
Rule 2: Zeros between non-zero digits count
3007 has 4 sig figs. 90.5 has 3. 5.0630 has 5. A zero locked between real digits is always significant, no matter where the decimal sits.
Rule 3: Leading zeros never count
0.0047 has 2 sig figs. 0.000081 has 2. 0.0002050 has 4. Zeros in front of the first non-zero digit only set the decimal position, they carry no measurement information.
Rule 4: Trailing zeros count only with a decimal point
2000 has 1 sig fig. 2000. has 4. 45.00 has 4. 0.00300 has 3. The decimal point is the switch that turns trailing zeros on.
Are leading zeros significant?
No. Leading zeros are never significant. In 0.0043 the two zeros after the decimal do nothing but mark place value, so the number has 2 sig figs. The same holds for 0.000081 (2 sig figs) and 0.00450 (3 sig figs, because the last zero is a trailing zero after the decimal, not a leading one). The trick is to find the first non-zero digit and start counting there.
Are trailing zeros significant?
Only when a decimal point is present. 500 has 1 sig fig, but 500. has 3 and 500.0 has 4. In 0.070 the trailing zero counts (2 sig figs) because it comes after the decimal. In 900 the trailing zeros do not count (1 sig fig) because there is no decimal. When a plain whole number like 5000 is genuinely precise to all four digits, scientific notation such as 5.000 × 103 removes the ambiguity.
How many sig figs in scientific notation?
Only the digits in front of the × 10 part count. The power of ten never affects the sig fig count.
- 4.20 × 103 has 3 sig figs (4, 2, 0).
- 6.02 × 1023 has 3 sig figs (6, 0, 2).
- 3.40 × 105 has 3 sig figs (3, 4, 0).
- 5.0630 × 104 has 5 sig figs (5, 0, 6, 3, 0).
This is why scientists write measurements this way. It makes the exact number of significant figures impossible to misread.
How do you round to significant figures?
Keep the digits up to the position you want, then look at the next digit to decide rounding. If it is 5 or higher, round up. Below 5, round down. Large numbers often need scientific notation so the sig fig count stays clear. Here are the exact rounding questions people search, worked out.
| Round this | To sig figs | Answer |
|---|---|---|
| 45.5147 | 4 | 45.51 |
| 865250 | 4 | 865300 (8.653 × 105) |
| 0.0637 | 2 | 0.064 |
| 3961 | 2 | 4000 (4.0 × 103) |
| 0.02315621 | 3 | 0.0232 |
| 4.62 | 1 | 5 |
| 274 | 1 | 300 (3 × 102) |
| 1047.78 | 3 | 1050 (1.05 × 103) |
| 3658.4586 | 5 | 3658.5 |
| 26814 | 3 | 26800 (2.68 × 104) |
| 2530 | 1 | 3000 (3 × 103) |
| 6789 | 3 | 6790 (6.79 × 103) |
A note on 865250. Rounded to 4 sig figs it becomes 865300, which the tool may display as 8.653 × 105. Both mean the same thing. Scientific notation removes the doubt about whether those last zeros are significant.
How many sig figs does the answer keep when multiplying or dividing?
The answer keeps the same number of significant figures as the input with the fewest. Multiply first, then round the final result. Do not round in the middle.
3.42 × 0.056
Raw result: 0.19152
3.42 has 3 sig figs, 0.056 has 2. The smaller count is 2.
Final answer: 0.19
85.334 ÷ 6.2
Raw result: 13.7635…
85.334 has 5 sig figs, 6.2 has 2. The smaller count is 2.
Final answer: 14
67.6 × 1.2
Raw result: 81.12
67.6 has 3 sig figs, 1.2 has 2. The smaller count is 2.
Final answer: 81
0.98 × 45.3
Raw result: 44.394
0.98 has 2 sig figs, 45.3 has 3. The smaller count is 2.
Final answer: 44
How many sig figs when adding or subtracting?
Here the rule changes. Addition and subtraction keep the fewest decimal places, not the fewest sig figs. Line the numbers up at the decimal point and the answer can only be as precise as the least precise input. Mixing this rule up with the multiplication rule is the single most common sig fig mistake.
12.77 + 0.8
Raw result: 13.57
0.8 has just 1 decimal place, so the answer keeps 1.
Final answer: 13.6
24.89 − 21
Raw result: 3.89
21 has 0 decimal places, so the answer keeps 0.
Final answer: 4
75.901 + 26.1
Raw result: 102.001
26.1 has 1 decimal place, so the answer keeps 1.
Final answer: 102.0
6325.23 + 1.16398
Raw result: 6326.39398
6325.23 has 2 decimal places, so the answer keeps 2.
Final answer: 6326.39
Sig figs in chemistry
In chemistry, significant figures show how precise a measurement actually is. You report every digit you know for certain plus one estimated digit. When you run molarity, dilution, or reaction yield calculations, the answer cannot claim more precision than your least precise measurement. That is why a mass read as 0.0250 g (3 sig figs) limits the result even if your other values have five or six. Report too many digits and you are claiming accuracy your equipment never gave you.
Sig figs in physics
Physics uses the same rules, but the stakes show up in unit-heavy calculations. If you measure a distance as 2.5 m and a time as 2.500 s, those are different statements, the first is precise to the tenth, the second to the thousandth. When you divide to get speed, the answer follows the multiplication and division rule and keeps the fewer sig figs of the two. Reporting a velocity to six decimal places from a measurement good to two figures is not more accurate, it is just wrong.
Common sig fig mistakes
Five errors show up more than any others:
- Counting leading zeros. 0.0043 has 2 sig figs, not 4. The zeros only place the decimal.
- Assuming every zero is insignificant. 20.0 has 3, not 1. The decimal changes everything.
- Ignoring the decimal point. 5000 has 1 sig fig, but 5000. has 4.
- Counting the exponent in scientific notation. 3.40 × 105 has 3 sig figs. The power of ten does not count.
- Rounding too early. Round only at the final answer, never in the middle of a multi-step problem.
Do exact numbers affect sig figs?
No. Counted or defined values, like 12 eggs in a dozen or 100 cm in a metre, have unlimited significant figures. They never limit your answer. Only measured values carry sig fig limits, because only measurements have uncertainty. This is why conversion factors do not reduce the precision of a calculation.
Why significant figures matter
Sig figs stop you from claiming false precision. A reading of 2.5 cm and a reading of 2.500 cm are not the same statement, the second says you measured to the thousandth. In lab reports, engineering specs, and any calculation built on measured data, sig figs keep your reported numbers honest about how much you actually know. Report the right count and your data stays credible.
Once you are comfortable with sig figs, the same rounding logic shows up in order-of-operations problems in the BODMAS calculator and in log calculations, where you often round results to a set number of figures.
Frequently asked questions
How do you calculate sig figs?
Find the first non-zero digit and start counting from there. Count every non-zero digit, every zero between non-zero digits, and every trailing zero that follows a decimal point. Ignore leading zeros. For 0.00453 the answer is 3, and for 30.00 it is 4.
Is 0 a significant figure?
Sometimes. A zero counts when it sits between non-zero digits (like the 0 in 6.02) or when it is a trailing zero after a decimal point (like the zeros in 20.0). A zero does not count when it is a leading zero (0.0056) or a trailing zero in a whole number with no decimal (5000).
How many sig figs should my answer have?
It depends on the operation. For multiplication and division, match the input with the fewest significant figures. For addition and subtraction, match the input with the fewest decimal places. Round only once, at the very end.
How do you round to a certain number of sig figs?
Keep digits up to the position you need, then look at the next digit. Round up if it is 5 or more, down if it is less. For example, 45.5147 to 4 sig figs is 45.51, and 0.0637 to 2 sig figs is 0.064.
Do exact or counted numbers have sig figs?
Exact numbers, like a count of items or a defined conversion factor, have unlimited sig figs and never limit the precision of your answer. Only measured values carry a sig fig limit.
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