This sig fig calculator does the two things chemistry and physics classes actually require: count how many significant figures a number has, and round a number to a chosen number of significant figures. It also names the rule that applied, which is the part students lose marks on.
It works as a significant figures calculator, a sig figs calculator or a sigfig calculator, since those are all the same tool under different spellings.
Significant figures encode how precisely a value was measured. Writing 2.50 g claims you measured to the hundredth of a gram. Writing 2.5 g claims only tenths. That is why sig figs survive every calculation rule in science: they stop you inventing precision your instruments never had.
The terms significant figures, significant digits and sig figs all mean the same thing. Chemistry courses tend to say sig figs, maths textbooks say significant digits, and the rules are identical either way.
The Five Rules for Counting Sig Figs
Every case reduces to these five rules:
- Non-zero digits are always significant: 123 has 3
- Zeros between non-zero digits are always significant: 1002 has 4
- Leading zeros are never significant: 0.00520 has 3 (the 5, the 2 and the trailing 0)
- Trailing zeros after a decimal point are significant: 12.300 has 5
- Trailing zeros with no decimal point are ambiguous, and conventionally not significant: 1200 has 2
Only the last rule causes real trouble, and it is the reason scientific notation exists. To make trailing zeros count in a whole number, write 1.200 × 10³, which has an unambiguous 4 sig figs. Every digit in the mantissa of a number in scientific notation is significant, with no exceptions to remember.
An alternative for whole numbers is a trailing decimal point: 1200. means all four digits are significant. It is valid but easy to miss when reading, so scientific notation is safer.
How Many Sig Figs Is That?
The single most searched case is 100, and the honest answer is that it depends on how it was written. As plain 100 the convention gives 1 significant figure. As 100. it is 3, and as 100.0 it is 4. This is not a trick: the notation is genuinely carrying less information than the measurement did, which is exactly the problem scientific notation solves.
The pattern to internalise is that a decimal point anywhere in the number makes every trailing zero significant. No decimal point means trailing zeros are placeholders.
| Number | Sig figs | Why |
|---|---|---|
| 100 | 1 (ambiguous) | Trailing zeros, no decimal point. Write 1.00 × 10² for 3, or 100. for 3 |
| 100. | 3 | The trailing decimal point makes both zeros significant |
| 100.0 | 4 | Decimal point present, so every trailing zero counts |
| 1000 | 1 (ambiguous) | Same rule as 100. Write 1.000 × 10³ for 4 |
| 10 | 1 (ambiguous) | Conventionally 1. Write 10. or 1.0 × 10¹ for 2 |
| 10.0 | 3 | Decimal point present |
| 20.0 | 3 | Decimal point present |
| 1.00 | 3 | Trailing zeros after a decimal point are significant |
| 0.01 | 1 | Leading zeros never count, so only the 1 is significant |
| 0.0100 | 3 | The 1 plus two trailing zeros after the decimal point |
| 2.025 | 4 | All non-zero digits, plus a captive zero between them |
| 0.00520 | 3 | Leading zeros excluded, trailing zero included |
| 1200 | 2 (ambiguous) | Write 1.200 × 10³ for 4, or 1200. for 4 |
Ambiguous means the written form does not tell you the precision. In coursework, assume the conventional reading (trailing zeros without a decimal point do not count) unless your textbook says otherwise, and write your own answers in scientific notation so the question never arises.
Sig Fig Rules: Addition, Subtraction, Multiplication and Division
The addition sig fig rules and the multiplication sig fig rules are genuinely different rules, and swapping them is the most common error on coursework. Why they differ comes down to what the uncertainty attaches to. When you add, the absolute uncertainties add, so the coarsest decimal place dominates. When you multiply, the relative uncertainties add, so the fewest significant figures dominates.
A case worth seeing: 100.0 + 23.456 = 123.456, which rounds to 123.5. The answer has 4 sig figs even though one input had 5, because 100.0 is only precise to one decimal place.
Subtraction can destroy precision dramatically. 12.0 − 11.87 = 0.13, which must be reported as 0.1: two three- and four-figure measurements produced a result with a single significant figure. This is called catastrophic cancellation, and it is the reason experiments avoid measuring small differences between large numbers.
In multi-step problems, carry extra digits through and round only at the end. Rounding each intermediate step compounds the error, which is the opposite of what the rules are for.
| Operation | Rule | Worked example |
|---|---|---|
| Addition and subtraction | Keep the fewest DECIMAL PLACES of any input | 12.11 + 18.0 + 1.013 = 31.123 → 31.1 (18.0 has 1 dp) |
| Subtraction | Same decimal-places rule | 12.0 − 11.87 = 0.13 → 0.1 (12.0 has 1 dp) |
| Multiplication and division | Keep the fewest SIG FIGS of any input | 2.5 × 3.42 = 8.55 → 8.6 (2.5 has 2 sig figs) |
| Division | Same sig-figs rule | 25.6 ÷ 4.0 = 6.4 → 6.4 (4.0 has 2 sig figs) |
| Exact numbers | Never limit the result | 3 apples × 2.50 g = 7.50 g (the count 3 is exact) |
Addition counts decimal places. Multiplication counts significant figures. Those are different things, and swapping them is where most marks are lost.
Rounding to N Significant Figures
Find the Nth significant digit, then round based on the digit immediately after it:
- 233.356 to 2 sig figs → 230, because the third digit is 3 so the 3 stays
- 233.356 to 3 sig figs → 233
- 3.14159 to 3 sig figs → 3.14
- 0.0025349 to 3 sig figs → 0.00253
- 0.004567 to 2 sig figs → 0.0046
- 98,765 to 2 sig figs → 99,000, better written 9.9 × 10⁴
- 9.99 to 2 sig figs → 10., where the trailing decimal point matters
The last two cases are worth pausing on. In 99,000 the trailing zeros are placeholders rather than precision, which is why the scientific-notation form is preferred after rounding a whole number. And rounding 9.99 to 2 sig figs pushes the value up a digit to 10, where the zero must be marked significant or you have silently reported 1 sig fig instead of 2.
Sig Figs in Logs vs Exponents, and in pH
Logarithms follow a rule of their own, and the log sig fig rules catch nearly everyone in a first chemistry course. For a logarithm, the number of decimal places in the result equals the number of significant figures in the input:
- log(2.0 × 10³) = 3.301029... → 3.30, because 2.0 has 2 sig figs, so the answer gets 2 decimal places
- The digits before the decimal point (the 3 here) come from the power of ten. They locate the value rather than measure it, so they are not significant
This is exactly why pH is written the way it is. pH is defined as the negative log of the hydrogen-ion concentration, so:
- [H⁺] = 1.0 × 10⁻³ M, which is 2 sig figs, gives pH = 3.00, with 2 decimal places
- [H⁺] = 4.5 × 10⁻⁸ M gives pH = 7.35
- A pH reported as 7.00 has 2 significant figures, not 3
That last point is the one to remember: a pH meter reading 7.00 is claiming two-figure precision in the concentration, not three.
Exponents work in reverse. Raising 10 to a power converts decimal places back into significant figures, so 10^2.30 = 199.5... reports as 2.0 × 10², carrying 2 sig figs from the 2 decimal places in the exponent.
Sig Fig Practice: Significant Figures Practice Problems
If a problem asks you to express a sum "to the appropriate number of significant figures", it is testing the addition rule, so count decimal places rather than significant figures. That single distinction accounts for most of the marks lost on sig fig questions.
On how to express significant figures in a written answer: use scientific notation whenever a trailing zero needs to count, and keep the units. Significant figures in chemistry carry the same rules as in physics and maths, with the pH and logarithm case above being the one genuine addition.
| Problem | Answer | Rule used |
|---|---|---|
| How many sig figs in 0.00408? | 3 | Leading zeros excluded, captive zero included |
| How many sig figs in 5200? | 2 (ambiguous) | Trailing zeros, no decimal point |
| How many sig figs in 5200.0? | 5 | Decimal point makes all trailing zeros count |
| How many sig figs in 0.070? | 2 | Leading zeros out, trailing zero after the point in |
| Round 0.0027495 to 3 sig figs | 0.00275 | Fourth digit is 9, so round the 4 up |
| Round 84,619 to 2 sig figs | 85,000 or 8.5 × 10⁴ | Third digit is 6, so round the 4 up |
| Round 0.08642 to 3 sig figs | 0.0864 | Fourth digit is 2, so the 4 stays |
| 4.20 + 11.7 | 15.9 | Addition: fewest decimal places is 1 |
| 12.0 − 11.87 | 0.1 | Subtraction: fewest decimal places is 1 |
| 3.00 × 4.5 | 14 | Multiplication: fewest sig figs is 2, so 13.5 → 14 |
| 250.0 ÷ 5.0 | 50. | Division: fewest sig figs is 2, so mark the zero |
| log(4.5 × 10⁻⁸) as a pH | 7.35 | Log: 2 sig figs in becomes 2 decimal places out |
Frequently Asked Questions
How many sig figs in 100?
Conventionally one, because trailing zeros with no decimal point are treated as placeholders rather than measured digits. Written as 100. it has 3, and as 100.0 it has 4. If you need 3 significant figures unambiguously, write 1.00 × 10².
How many sig figs in 1000?
Conventionally one, for the same reason as 100: no decimal point means the trailing zeros are ambiguous. Write 1000. for 4 significant figures, or 1.000 × 10³ to remove all doubt.
How many significant figures in 100.0?
Four. The decimal point makes every trailing zero significant, so the 1 and all three zeros count. Compare it with plain 100, which conventionally has just one.
How many sig figs in 0.01?
One. Leading zeros only locate the decimal point and are never significant, so only the 1 counts. Writing 0.0100 would give 3, because the two trailing zeros come after the decimal point.
What are the sig fig rules for addition and subtraction?
Keep as many decimal places as the least precise input, not as many significant figures. 12.11 + 18.0 + 1.013 = 31.123, and because 18.0 has only one decimal place the answer is 31.1. Subtraction uses the same rule.
What are the sig fig rules for multiplication and division?
Keep as many significant figures as the input with the fewest. 2.5 × 3.42 = 8.55, and because 2.5 has only 2 significant figures the answer is 8.6. Division works identically: 25.6 ÷ 4.0 = 6.4.
How do I round 233.356 to two significant figures?
The first two significant digits are 2 and 3. Look at the next digit, which is 3, and since it is below 5 the second digit stays. The answer is 230. Rounding the same number to 3 significant figures gives 233.
How many sig figs does a pH have?
Only the decimal places count. A pH of 7.00 has 2 significant figures, because the digit before the decimal point comes from the power of ten in the concentration rather than from a measurement. pH 3.00 corresponds to [H⁺] = 1.0 × 10⁻³ M, which is 2 significant figures.
How many sig figs does 0.00520 have?
Three: the 5, the 2 and the final 0. The leading zeros only locate the decimal point and are never significant, while the trailing zero after a decimal point is significant because it claims measured precision.
How many significant figures does 1200 have?
By convention two, the 1 and the 2. Trailing zeros in a whole number with no decimal point are ambiguous placeholders. Writing 1200. makes it 4 significant figures, and 1.20 × 10³ makes it unambiguously 3.
Do leading zeros count as significant figures?
Never. In 0.0042 only the 4 and 2 are significant, and the zeros just position the decimal point. Scientific notation makes this obvious: 0.0042 is 4.2 × 10⁻³, and the leading zeros disappear entirely.
Are significant figures and significant digits the same thing?
Yes, they are two names for the same concept, and the counting rules are identical. Chemistry and physics courses usually say significant figures or sig figs, while mathematics and engineering texts often say significant digits.
Why do significant figures matter?
They communicate measurement precision honestly. If a scale reads to 0.1 g, reporting 2.5473 g invents precision that does not exist, while reporting 2.5 g states exactly what you know. Through a multi-step calculation the rules keep the final answer from claiming more certainty than the weakest measurement supports.