Significant Figures: The Rules That Actually Matter
Significant figures show how precisely a value is known. Getting them right keeps your answer honest — neither claiming more precision than your data supports nor throwing precision away. They are not busywork: they communicate the quality of a measurement.
Counting significant figures
- All non-zero digits are significant.
- Zeros between non-zero digits are significant: 1002 has four.
- Leading zeros are never significant: 0.0045 has two.
- Trailing zeros count only with a decimal point: 1500 has two, but 1500. and 1.500 × 10³ have four.
- In scientific notation, every digit in the mantissa is significant.
| Number | Sig figs | Why |
|---|---|---|
| 0.00420 | 3 | Leading zeros ignored, trailing zero after decimal counts |
| 1002 | 4 | Zeros trapped between non-zero digits count |
| 1500 | 2 | Trailing zeros, no decimal point |
| 1.500 × 10³ | 4 | Every mantissa digit is significant |
The ambiguous case: trailing zeros
A number like 1500 is genuinely ambiguous — it could mean two, three or four significant figures depending on how it was measured. Scientific notation removes the doubt: write 1.5 × 10³ for two, 1.50 × 10³ for three, or 1.500 × 10³ for four. When precision matters, scientific notation is the honest way to write it.
Rounding in calculations
There are two separate rules, and which one you use depends on the operation:
- Multiplication and division: the answer keeps the same number of significant figures as the input with the fewest. 4.56 × 1.4 = 6.4 (two sig figs).
- Addition and subtraction: the answer keeps the same number of decimal places as the input with the fewest. 12.11 + 1.1 = 13.2 (one decimal place).
Round only at the end
Carry extra digits through every intermediate step and round just once, at the final answer. Rounding partway through lets small errors accumulate and can shift the last figure of your result. A good habit is to keep one or two guard digits in working values until the very end.
Exact numbers
Counting numbers and defined conversions are exact and never limit the answer — treat them as having infinite significant figures. Examples include 1000 mL = 1 L, the "2 mol" coefficient from a balanced equation, and counting 12 items. Only measured quantities carry uncertainty, so only they constrain the precision of a result.
Common mistakes
- Counting leading zeros as significant — they only mark the decimal place.
- Applying the sig-fig rule to addition when the decimal-place rule is the correct one.
- Rounding intermediate steps, which compounds error.
- Letting an exact conversion limit the answer, when exact numbers never do.
Count sig figs and round any value on the Significant Figures Calculator, and see correct rounding applied throughout How to Approach Stoichiometry.
The General Chemistry Workbook's worked examples model correct significant-figure use throughout.
Frequently Asked Questions
No. Leading zeros only mark the position of the decimal point and are never significant. The number 0.0045 has two significant figures, the 4 and the 5.
Trailing zeros are significant only when a decimal point is present. So 1500 has two significant figures, but 1500. and 1.500 × 10³ both have four. Scientific notation removes the ambiguity.
The answer keeps the same number of significant figures as the input value that has the fewest. For example, 4.56 × 1.4 rounds to 6.4, limited by the two significant figures in 1.4.
Addition and subtraction count decimal places, not significant figures. The answer keeps the same number of decimal places as the input with the fewest, so 12.11 + 1.1 rounds to 13.2.
No. Exact numbers such as counted items and defined conversions like 1000 mL = 1 L have infinite significant figures and never limit the precision of an answer. Only measured quantities constrain the result.
No. Carry extra digits through every intermediate step and round only the final answer. Rounding partway through lets small errors accumulate and can change the last digit of your result.