Laboratory and exam calculations require reporting results with a precision that matches the least precise measurement. Significant figures (sig figs) encode that precision; scientific notation makes it unambiguous.
Counting Significant Figures
| Rule | Example | Sig figs |
|---|---|---|
| Non-zero digits always count | 123.45 | 5 |
| Zeros between digits count | 1002 | 4 |
| Leading zeros do not count | 0.00456 | 3 |
| Trailing zeros in a decimal count | 12.300 | 5 |
| Trailing zeros with no decimal are ambiguous | 1500 | 2–4 |
Write 1.50 × 10³ if three significant figures are intended for 1500.
Arithmetic Rules
Multiplication / division: the result has as many sig figs as the factor with the fewest sig figs.
$2.5 × 3.42 = 8.6$ (2 sig figs from 2.5)
Addition / subtraction: the result matches the least precise decimal place.
$12.11 + 0.3 = 12.4$ (tenths place)
Scientific Notation
N \times 10^kwith $1 ≤ |N| < 10$ (normalized form). Examples:
- 0.000482 = 4.82 \times 10^{-4} (3 sig figs)
- 602{,}000{,}000{,}000{,}000{,}000{,}000{,}000 = 6.02 \times 10^{23} (Avogadro-scale counting)
Metric Prefixes
Combine scientific notation with SI prefixes (m, μ, n, k, M, …). See the Metric Prefixes Cheatsheet and Unit Conversion Factors.
Practice
Convert units with the Length Converter or browse Unit Conversion Factors and Metric Prefixes. For solution prep, use the Concentration Calculator and the Concentration & Dilution Cheatsheet.