Significant Figures Rules
All 7 rules for determining which digits are significant — each with plain-English explanations and worked examples.
Reviewed by the Sig Figs Calc Editorial Team · Last updated April 2025 · See methodology
What are significant figures?
Significant figures are the digits in a number that carry meaningful information about its precision. When you measure something in a lab — say, 4.56 grams — each digit tells you something real. But if you write 0.0034, the leading zeros are just placeholders. They tell you where the decimal goes, not how precise the measurement is.
The rules below define exactly which digits are significant in any number. Learn these 7 rules and you can correctly determine sig figs in every situation.
Quick reference table
| Rule | Digit type | Significant? | Example |
|---|---|---|---|
| 1 | Non-zero digits | ✅ Always | 4.56 → 3 sf |
| 2 | Zeros between non-zeros | ✅ Always | 1.002 → 4 sf |
| 3 | Leading zeros | ❌ Never | 0.0034 → 2 sf |
| 4 | Trailing zeros after decimal | ✅ Always | 1.200 → 4 sf |
| 5 | Trailing zeros, no decimal | ⚠️ Ambiguous | 1000 → 1–4 sf |
| 6 | Exact numbers | ∞ Unlimited | 12 eggs → ∞ |
| 7 | Scientific notation (coefficient) | ✅ Count coefficient | 3.40 × 10⁻³ → 3 sf |
Non-zero digits are always significant
Every digit from 1 to 9 is always significant, regardless of where it appears in the number. There are no exceptions to this rule.
Examples
Zeros between non-zero digits are significant
Zeros that are "captured" between two non-zero digits are always significant. They are sometimes called captive zeros or sandwiched zeros.
Examples
Leading zeros are never significant
Leading zeros — zeros that appear before the first non-zero digit — are never significant. They exist only to show the magnitude of the number. Moving the decimal or using scientific notation removes them entirely.
Examples
Trailing zeros after a decimal point are significant
When a number has a decimal point and ends in zeros, those trailing zeros are significant. They tell you the precision of the measurement — 1.200 is more precise than 1.2. A scientist writing 1.200 is communicating that the measurement is accurate to the thousandths place.
Examples
Trailing zeros in whole numbers are ambiguous
When a whole number ends in zeros and has no decimal point, you cannot tell if those zeros are significant or just placeholders. The number 1000 might mean "approximately one thousand" (1 sig fig) or it might mean the measurement is precise to the units place (4 sig figs). To remove ambiguity, add a decimal point (1000.) or use scientific notation (1.000 × 10³).
Examples
⚠️ How to remove the ambiguity
- Add a decimal point:
1000.= 4 sig figs - Use scientific notation:
1.000 × 10³= 4 sig figs - Use scientific notation with fewer digits:
1 × 10³= 1 sig fig
Exact numbers have unlimited significant figures
Some numbers are exact — they are counted rather than measured, or defined rather than derived. Exact numbers have unlimited significant figures and never limit the precision of a calculation. If you count 12 beakers, the 12 is exact and introduces no rounding error.
Examples
In scientific notation, only the coefficient counts
In scientific notation (A × 10ⁿ), only the coefficient A determines the number of significant figures. The exponent n just positions the decimal — it carries no sig fig information. This is one of the main reasons scientists prefer scientific notation: it removes all ambiguity about which digits are significant.
Examples
Common points of confusion
Q: Is 0 ever significant?
Yes — but only in specific positions. Zeros between non-zero digits (captive zeros) are always significant. Trailing zeros after a decimal point are always significant. Only leading zeros and ambiguous trailing zeros in whole numbers are not (or may not be) significant.
Q: How do I know if a trailing zero is significant?
Look for a decimal point. If the number has a decimal point, trailing zeros are significant (100.00 = 5 sig figs). If there is no decimal point, they are ambiguous (100 = 1 to 3 sig figs). When in doubt, use scientific notation to be explicit.
Q: Does the number of sig figs change when I round?
Rounding adjusts the number to a target sig fig count. The result should display exactly that many sig figs. For example, rounding 3.456 to 2 sig figs gives 3.5 — which has 2 sig figs.
Frequently asked questions
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