Significant Figures Calculator Guide: Sig Fig Rules Explained (2026)
Quick Answer
Significant figures (sig figs) are the meaningful digits in a measurement that convey precision. The number 0.00340 has 3 sig figs (3, 4, 0 after decimal). Rules: non-zero digits always count, zeros between non-zero digits count, trailing zeros after a decimal count, leading zeros never count. For multiplication/division, round to the fewest sig figs in the problem.
What Are Significant Figures?
Significant figures — also called sig figs or significant digits — are the digits in a number that carry meaningful information about its precision. Every time you measure something in science, engineering, or everyday life, your measurement has a limit to how precise it can be. Sig figs are the way we communicate that limit in writing.
Consider the difference between writing “the table is 1 meter long” versus “the table is 1.00 meters long.” The first suggests precision to the nearest meter. The second implies you measured to the nearest centimeter and confirmed the length is exactly 1.00 m — not 0.99 m or 1.01 m. That distinction matters enormously in a chemistry lab, a construction project, or an engineering calculation.
According to the National Institute of Standards and Technology (NIST), uncertainty in measurement must always be reported explicitly, and significant figures are the standard method for doing so in routine calculations. Reporting too many sig figs implies false precision; reporting too few loses information.
Real-world example: a kitchen scale that reads “52.3 g” has three significant figures and a precision of ±0.1 g. A laboratory analytical balance reading “52.3041 g” has six significant figures and a precision of ±0.0001 g. These are very different instruments, and sig figs make that difference explicit without needing a footnote.
The 5 Rules for Counting Significant Figures
The College Board AP Chemistry curriculum lists five core rules for identifying significant figures. Master these and you can handle any number.
Rule 1 — Non-Zero Digits Always Count
Every digit from 1 through 9 is always significant, no exceptions. The number 4,832 has four sig figs. The number 7.15 has three sig figs.
Rule 2 — Trapped (Sandwiched) Zeros Always Count
A zero that sits between two non-zero digits is significant. Examples: 1,007 has four sig figs (the two zeros are trapped). 30.8 has three sig figs (the zero is between 3 and 8). 1,000,001 has seven sig figs.
Rule 3 — Trailing Zeros After a Decimal Point Always Count
If a number has a decimal point and zeros appear at the end, those zeros are significant. They were written deliberately to communicate precision. Examples: 2.300 has four sig figs. 0.00500 has three sig figs (the 5 and the two trailing zeros). 100.0 has four sig figs.
Rule 4 — Trailing Zeros Without a Decimal Point Are Ambiguous
The number 1,500 is ambiguous: it might have 2, 3, or 4 sig figs depending on how it was measured. Scientific notation eliminates the ambiguity. Writing 1.5 × 10³ indicates 2 sig figs; 1.50 × 10³ indicates 3; 1.500 × 10³ indicates 4. When in doubt, use scientific notation to be explicit.
Rule 5 — Leading Zeros Never Count
Zeros that appear before the first non-zero digit are just placeholders — they tell you the scale of the number, not its precision. Examples: 0.0047 has two sig figs (4 and 7). 0.00340 has three sig figs (3, 4, and the trailing zero after the 4). 0.1 has one sig fig.
Sig Figs in Addition and Subtraction
For addition and subtraction, the rule is based on decimal places, not total significant figures. Your answer can only be as precise as the least precise measurement in the problem — meaning the one with the fewest decimal places.
Worked example:
| Number | Decimal Places |
|---|---|
| 12.11 | 2 |
| 18.0 | 1 |
| 1.013 | 3 |
| Sum = 31.123 | Round to 1 decimal place |
| Answer = 31.1 |
The limiting value is 18.0, which has only one decimal place. So the answer rounds to 31.1, not 31.123. The extra digits in 12.11 and 1.013 cannot make the answer more precise than 18.0 allows.
Another example: 100.5 + 23.45 + 0.006 = 123.956 → rounds to 124.0 (one decimal place, limited by 100.5).
According to the IUPAC Green Book(Quantities, Units and Symbols in Physical Chemistry), addition and subtraction require alignment of decimal places to determine the correct precision of the result — the same principle underlying this rule.
Sig Figs in Multiplication and Division
For multiplication and division, the rule switches to total significant figures. The answer gets the same number of sig figs as the measurement with the fewest sig figs.
Worked example:
| Operation | Sig Figs |
|---|---|
| 4.56 (3 sig figs) | 3 |
| × 1.4 (2 sig figs) | 2 |
| Calculator result = 6.384 | Limit: 2 sig figs |
| Answer = 6.4 |
Because 1.4 has only 2 sig figs, the answer 6.384 must be rounded to 2 sig figs: 6.4.
Division works the same way. 8.20 ÷ 2.5 = 3.28 → rounds to 3.3 (2 sig figs, limited by 2.5).
A common pitfall: exact numbers (like defined constants or counts) have infinite significant figures and do not limit your answer. If a recipe calls for doubling (multiplying by exactly 2), that 2 is not a measurement — it's exact. Only measured values with uncertainty limit your sig figs.
Scientific Notation and Sig Figs
Scientific notation is the cleanest way to express a number with a specific number of significant figures, especially when trailing zeros create ambiguity.
The format is: M × 10^n, where M is a number between 1 and 10 (the coefficient) and n is an integer exponent. Every digit written in M is significant.
| Standard Form | Scientific Notation | Sig Figs |
|---|---|---|
| 1500 | 1.5 × 10³ | 2 |
| 1500 | 1.50 × 10³ | 3 |
| 1500 | 1.500 × 10³ | 4 |
| 0.00340 | 3.40 × 10²–² | 3 |
| 602,200,000,000,000,000,000,000 | 6.022 × 10²³ | 4 |
Avogadro's number (6.022 × 10²³) is a classic example. Writing it as 602,200,000,000,000,000,000,000 tells you nothing about precision — scientific notation makes clear there are 4 sig figs. The 2018 CODATA recommended value is 6.02214076 × 10²³ mol¹–, giving 9 significant figures.
To convert a number to scientific notation: move the decimal point until there is exactly one non-zero digit to the left. The number of places you moved the decimal becomes the exponent (positive if you moved left, negative if you moved right).
Examples: 4,500,000 → 4.5 × 10&sup6;. 0.000078 → 7.8 × 10&sup5;–.
Common Significant Figures Examples
The table below covers 20 common numbers and shows how many significant figures each has.
| Number | Sig Figs | Reason |
|---|---|---|
| 7 | 1 | Single non-zero digit |
| 42 | 2 | Two non-zero digits |
| 100 | 1 (ambiguous) | Trailing zeros, no decimal |
| 100. | 3 | Decimal point makes all digits significant |
| 100.0 | 4 | Trailing zero after decimal counts |
| 0.005 | 1 | Leading zeros are placeholders |
| 0.00340 | 3 | 3, 4, and trailing zero count; leading zeros don't |
| 1,007 | 4 | Trapped zeros always count |
| 2.500 | 4 | All trailing zeros after decimal count |
| 0.1010 | 4 | 1, 0 (trapped), 1, 0 (trailing) — all count |
| 30.8 | 3 | Zero trapped between 3 and 8 |
| 3,600 | 2 (ambiguous) | Trailing zeros without decimal are ambiguous |
| 3,600. | 4 | Decimal point indicates all digits are significant |
| 3.60 × 10³ | 3 | Scientific notation: 3, 6, 0 — all significant |
| 0.000120 | 3 | 1, 2, trailing zero — leading zeros don't count |
| 9.80 | 3 | 9, 8, and trailing zero all count |
| 1,000,000 | 1 (ambiguous) | Use scientific notation to clarify |
| 1.000 × 10&sup6; | 4 | Scientific notation removes ambiguity |
| 500.10 | 5 | 5, 0 (trapped), 0 (trapped), 1, 0 (trailing) |
| 6.022 × 10²³ | 4 | Avogadro's number expressed to 4 sig figs |
Why Sig Figs Matter: The Precision Problem
Significant figures are not just a classroom formality. They prevent a phenomenon called false precision— reporting a result with more certainty than your measurements actually support.
Imagine measuring a room with a tape measure accurate to the nearest inch. You get 12 feet 3 inches × 9 feet 7 inches. A calculator gives you 117.604 square feet. But your measurements were only precise to about ±0.5 inches, so the answer is properly reported as 118 square feet (3 sig figs). Writing 117.604 sq ft implies you measured with millimeter precision — which you did not.
In multi-step calculations, rounding errors can compound. Good practice — endorsed by most physics and chemistry textbooks including Zumdahl's Chemistry and Serway's Physics— is to carry one or two extra digits through intermediate calculations and round only at the final answer.
The U.S. National Institute of Standards and Technology (NIST) Technical Note 1297 on measurement uncertainty states that “the number of figures used to express a measured quantity should be consistent with its uncertainty.” That is the scientific foundation for sig fig rules.
Count sig figs and round results instantly
Use the Free Significant Figures Calculator →Frequently Asked Questions
How many significant figures does 0.00340 have?
0.00340 has 3 significant figures: the digits 3, 4, and the trailing zero after the 4. The leading zeros (0.00) are just placeholders and do not count as significant figures.
Do zeros count as significant figures?
It depends on the zero's position. Trapped zeros (between two non-zero digits) always count. Trailing zeros after a decimal point count. Leading zeros never count. Trailing zeros without a decimal point are ambiguous — scientific notation removes the ambiguity.
How do you round to significant figures?
Identify the digit at the position of the last significant figure you want to keep. Look at the next digit to the right. If it is 5 or greater, round the kept digit up by 1. If it is less than 5, leave the kept digit unchanged. Replace all digits to the right with zeros (or drop them if they are after a decimal).
When multiplying or dividing, how many sig figs should the answer have?
The answer should have the same number of significant figures as the measurement with the fewest sig figs. For example, 4.56 (3 sig figs) × 1.4 (2 sig figs) = 6.384, which rounds to 6.4 (2 sig figs).
When adding or subtracting, how many decimal places should the answer have?
The answer should have the same number of decimal places as the measurement with the fewest decimal places (not fewest sig figs). For example, 12.11 + 18.0 + 1.013 = 31.123, which rounds to 31.1 because 18.0 has only 1 decimal place.
Why do significant figures matter in science?
Significant figures communicate the precision of a measurement. Writing 3.0 cm instead of 3 cm tells the reader the measurement is precise to the nearest 0.1 cm. Reporting more sig figs than your instrument can measure implies false precision, which can lead to compounding errors in multi-step calculations. NIST and IUPAC both require appropriate use of significant figures in published scientific data.