What Are Significant Figures?
Significant figures, often called sig figs or significant digits, are the digits in a measured value that communicate its precision. Nonzero digits are significant, while zeros can be significant or simply act as placeholders depending on where they appear.
For example, 12.5 contains three significant figures. The leading zeros in 0.00456 are not significant, so that number contains three significant figures. A zero between nonzero digits is significant, so 2.08 has three significant figures.
How to Use the Sig Fig Calculator
- Enter a whole number, decimal, or scientific-notation value.
- For arithmetic, enter an expression such as 4.18 * 3.14.
- Enter the number of significant figures required for the rounded result.
- Select Calculate Sig Figs to see the count, rounded value, scientific notation, and E notation.
Rules for Counting Significant Figures
| Rule | Example | Sig figs |
|---|---|---|
| Nonzero digits are significant. | 456 | 3 |
| Leading zeros are placeholders. | 0.00456 | 3 |
| Zeros between nonzero digits count. | 2.08 | 3 |
| Trailing decimal zeros count. | 100.00 | 5 |
| Trailing zeros in a whole number can be ambiguous. | 100 | Usually 1 without more context |
Significant Figures in Calculations
For multiplication and division, the final answer is generally reported with the same number of significant figures as the input with the fewest significant figures. For example, 4.321 × 3.14 = 13.56974, which is reported as 13.6 when three significant figures are required.
For addition and subtraction, round the result to the least precise decimal place in the numbers being combined. For example, 128.1 + 1.72 + 0.457 = 130.277, which is reported as 130.3.
Examples of Rounding to Significant Figures
24.0725 → 3 sig figs
24.1
0.004562 → 2 sig figs
0.0046
3,453,528 → 4 sig figs
3,454,000
2648 → 3 sig figs
2,650
Why Sig Figs Matter
Significant figures help prevent a calculated answer from implying more measurement precision than the original data supports. They are especially useful in laboratory work, chemistry, physics, engineering, and other measurement-based calculations.
Scientific Notation and Significant Figures
Scientific notation makes significant figures easier to communicate. For example, 1.000 × 10³ clearly represents four significant figures, while an unqualified whole number such as 1000 can be ambiguous.