Short Answer
Avogadro’s number is often introduced as 6.022 × 1023, but that shorthand hides a crucial distinction. Since the 2019 revision of the International System of Units (SI), the Avogadro constant NA is an exact defined constant: 6.02214076 × 1023 mol−1. The dimensionless Avogadro number is likewise exact. Yet many quantities used with it — mass, volume, amount concentration, and molar mass — are measured. This article explains when Avogadro’s number limits significant figures and when it does not.
This site is a precision-and-rounding reference, not merely a significant figures calculator. The calculator is useful, but the rules, standards, and examples below are the core of the resource. For related material, see Exact Numbers, Significant Figures, and Why Sig Figs Are an Approximation.
Rule Statement
Use this rule: exact numbers and defined constants have infinite significant figures and never limit the precision of a calculation. Measured quantities have finite significant figures and do limit the result. The Avogadro constant belongs to the first group in the current SI.
Formally, the mole is defined by fixing the numerical value of the Avogadro constant to exactly 6.02214076 × 1023 when expressed in mol−1. Therefore:
- NA = 6.02214076 × 1023 mol−1 (exact, by definition).
- The Avogadro number = 6.02214076 × 1023 (exact, dimensionless).
- Any experimental realization of the mole — for example, determining the amount of substance from a measured mass and molar mass — carries measurement uncertainty.
- If you replace the exact constant with 6.022 × 1023, you are using a rounded approximation, not the exact constant. That approximation may limit the result if the other data have more significant figures.
Key distinction: The constant is exact. The process of measuring a sample is not. The exact constant does not add uncertainty; the measured sample data does.
Convention Comparison Table
| Quantity or value | Status | Significant-figure rule | Example |
|---|---|---|---|
| Avogadro constant NA | Exact defined constant (SI, 2019) | Infinite sig figs; never limiting | 6.02214076 × 1023 mol−1 |
| Avogadro number | Exact dimensionless number | Infinite sig figs; never limiting | 6.02214076 × 1023 |
| Molar mass of a real sample | Usually measured or evaluated with uncertainty | Finite sig figs; limiting | 18.015 g mol−1 for water, depending on source |
| Mass of a sample | Measured | Finite sig figs; limiting | 2.50 g |
| Counted entities | Exact count if truly counted | Infinite sig figs; not limiting | 12 atoms counted individually |
| Pre-2019 CODATA value | Measured with uncertainty | Finite sig figs; limiting | 6.022140857(74) × 1023 mol−1 |
| Rounded display value 6.022 × 1023 | Approximation of an exact constant | Treat as 4 sig figs if used numerically | 6.022 × 1023 mol−1 |
For broader rounding conventions, compare Rounding Rules and Scientific Notation.
Worked Examples
Example 1: Molecules in a measured amount
How many molecules are in 2.50 mol of water? The value 2.50 mol has three significant figures. The Avogadro constant is exact, so it does not limit the result.
- Write the conversion: N = (2.50 mol)(6.02214076 × 1023 mol−1).
- Multiply: (2.50)(6.02214076) = 15.0553519.
- Attach the power: 15.0553519 × 1023 = 1.50553519 × 1024.
- Round to three significant figures because 2.50 has three: 1.51 × 1024 molecules.
Notice that the exact constant could be written with 20 digits, and the answer would still be 1.51 × 1024. Only the measured 2.50 mol limits the precision.
Example 2: Atoms to moles
A sample contains 3.01 × 1023 atoms. Convert to moles. The count is given as 3.01 × 1023, so it has three significant figures. The conversion uses the exact Avogadro constant.
- Set up: n = (3.01 × 1023 atoms) / (6.02214076 × 1023 atoms mol−1).
- Divide: 3.01 / 6.02214076 = 0.499822…
- Round to three significant figures: 0.500 mol.
If a historical measured value of NA were used instead, its uncertainty would enter the result. Under the current SI, the conversion factor itself is exact.
Example 3: Mass to molecules with measured molar mass
Calculate the number of water molecules in 1.00 g of water, using M(H2O) = 18.015 g mol−1. Both 1.00 g and 18.015 g mol−1 are measured or conventionally evaluated quantities with finite significant figures. The exact Avogadro constant does not limit the result.
- Amount: n = 1.00 g / 18.015 g mol−1 = 0.055509… mol.
- Molecules: N = (0.055509… mol)(6.02214076 × 1023 mol−1) = 3.3428… × 1022.
- The limiting input has three significant figures, so report 3.34 × 1022 molecules.
Counter-Examples
- Wrong: ‘Avogadro’s number has 9 significant figures, so my answer must have 9 significant figures.’ Why it is wrong: The exact constant has infinite significant figures; it does not force extra precision.
- Wrong: ‘The current Avogadro constant is 6.02214076 × 1023 mol−1 with an uncertainty, so I must propagate that uncertainty.’ Why it is wrong: That numerical value is exact by SI definition. Uncertainty belongs to experimental realization, not to the constant.
- Wrong: Rounding 6.02214076 × 1023 to 6.0 × 1023 before a calculation and then treating 6.0 as exact. Why it is wrong: You have introduced avoidable rounding error. Use the exact value in the calculation, then round once at the end.
- Wrong: Reporting 1.50553519 × 1024 molecules from 2.50 mol. Why it is wrong: The measured amount has three significant figures, so the final answer should have three.
For more on avoiding these issues, see Rounding vs Significant Figures and Double Rounding Error.
Standards Citation
The exact status of the Avogadro constant follows from the SI defining constants. Key references include:
- BIPM, SI Brochure, 9th edition (2019), Section 2.3.1. Defines the mole by fixing the numerical value of the Avogadro constant to exactly 6.02214076 × 1023 mol−1.
- NIST SP 330 (2019), Section 2.3.1. U.S. edition of the SI Brochure; same definition and exact status.
- JCGM 100:2008 (GUM), Clauses 3.3.2 and 5.1.2. Discusses exact quantities and the reporting of measurement results with an appropriate number of digits.
- ISO 80000-1:2009, Clauses 6.4–6.5. Provides general rules for rounding and significant figures in quantity values.
- ASTM E29-22, Sections 4–7. Standard practice for using significant digits in test data and determining conformance.
Common Mistakes
- Confusing the Avogadro constant with the Avogadro number. The constant has unit mol−1; the number is dimensionless. Both are exact in the current SI when written with the defined value.
- Treating 6.022 × 1023 as the exact constant. It is a rounded display value. Use the full defined value when precision matters.
- Letting an exact conversion factor limit significant figures. Exact conversions — including NA, 1 mol = 6.02214076 × 1023 entities, and 1 km = 1000 m — do not limit.
- Propagating historical uncertainty for the modern constant. Before 2019, NA was measured. Since 2019, it is defined.
- Forgetting that sample mass and molar mass are measured. These quantities usually determine the final significant figures in mole calculations.
- Rounding in the middle of a multi-step calculation. Keep extra digits until the final result, then round once. See Double Rounding Error.
Quick Reference Table
| Situation | Does it limit sig figs? | Reason |
|---|---|---|
| Using NA = 6.02214076 × 1023 mol−1 | No | Exact defined constant |
| Using 6.022 × 1023 as a deliberate approximation | Yes, at 4 sig figs | The rounded numerical value is finite |
| Using a measured mass such as 2.50 g | Yes, at 3 sig figs | Measured quantity |
| Using a counted set of 25 atoms | No | Exact count |
| Using molar mass 18.015 g mol−1 | Usually yes | Evaluated from measured atomic weights |
| Using 1 mol = 6.02214076 × 1023 entities | No | Exact definition of the mole |
Related Rules
- Exact Numbers — how exact values behave in calculations.
- Significant Figures — core counting and rounding rules.
- Rounding Rules — half-up, half-even, and convention choices.
- Measurement Uncertainty — why sig figs are a simplified uncertainty model.
- Chemistry — mole calculations, molar mass, and solution stoichiometry.
- Physics — constants, units, and dimensional analysis.
Sources & Further Reading
- BIPM. The International System of Units (SI), 9th ed. (2019). Section 2.3.1.
- NIST. NIST Special Publication 330: The International System of Units (SI) (2019). Section 2.3.1.
- JCGM. Evaluation of Measurement Data — Guide to the Expression of Uncertainty in Measurement (GUM), JCGM 100:2008.
- ISO. ISO 80000-1:2009 Quantities and units — Part 1: General. Clauses 6.4–6.5.
- ASTM. ASTM E29-22, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications.
For more precision guidance, explore GUM Guide, ISO 80000, and ASTM E29.
FAQ
Is Avogadro's number exact or measured?
In the current SI, the Avogadro constant is exact by definition: 6.02214076 × 10^23 mol^-1. Historically it was measured, and experimental realizations of the mole still involve measurement uncertainty.
Does Avogadro's number affect significant figures?
No, when used as the exact defined constant. It does not limit the number of significant figures. If you deliberately use a rounded version such as 6.022 × 10^23, that rounded value can limit the result.
Why do textbooks write 6.022 × 10^23?
For readability and because many introductory problems have three or four significant figures. The shorter form is an approximation of the exact value, not the exact constant itself.
How should I report a mole calculation?
Use the exact Avogadro constant in the calculation, keep guard digits, and round the final result according to the least precise measured input.
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