3 Significant Figures Calculator
Here’s a comprehensive table outlining the key concepts related to significant figures, including definitions, rules for identifying significant figures, examples, and common uses.
| Concept | Description | Examples |
|---|---|---|
| Definition of Significant Figures | Significant figures are the digits in a number that contribute to its accuracy. This includes all non-zero digits, zeros between significant digits, and trailing zeros in the decimal portion. | - 123.45 has 5 significant figures. - 0.00456 has 3 significant figures. |
| Rules for Identifying Significant Figures | 1. Non-zero digits are always significant. 2. Zeros between significant digits are significant. 3. Leading zeros (to the left of the first non-zero digit) are not significant. 4. Trailing zeros in a decimal number are significant. 5. Trailing zeros in a whole number without a decimal point are not significant. | - 4500 has 2 significant figures (if no decimal point). - 4500. has 4 significant figures (decimal indicates all are significant). |
| Examples of Counting Significant Figures | - 1.005: 4 significant figures. - 0.0023: 2 significant figures. - 600: 1 significant figure (without a decimal point). - 0.070: 2 significant figures. | |
| Rounding with Significant Figures | When rounding numbers, maintain the correct number of significant figures based on the rules. If the digit following the last significant figure is 5 or greater, round up. If it's less than 5, leave the last significant figure unchanged. | - Round 2.345 to 3 significant figures: 2.35. - Round 0.00456 to 2 significant figures: 0.0046. |
| Addition and Subtraction Rules | When adding or subtracting numbers, the result should be reported to the least number of decimal places of any number in the operation. | - 12.11 + 0.3 = 12.41 (reported as 12.4 with 1 decimal place). |
| Multiplication and Division Rules | When multiplying or dividing numbers, the result should have the same number of significant figures as the factor with the least number of significant figures. | - 4.56 × 1.4 = 6.384 (reported as 6.4 with 2 significant figures). |
| Common Uses of Significant Figures | Significant figures are used in scientific measurements, calculations, and reporting results to ensure precision and accuracy in communication. | - Scientific experiments and data analysis require significant figures for precision. |
Summary of Rules for Significant Figures:
- Non-zero digits are significant.
- Leading zeros are not significant.
- Captive zeros (between non-zero digits) are significant.
- Trailing zeros in decimal numbers are significant.
- Trailing zeros in whole numbers without a decimal point are not significant.
Practice Examples
- Count the significant figures in the following numbers:
- 0.00450: 3 significant figures.
- 100.2: 4 significant figures.
- 4500.: 4 significant figures.
- 0.00340: 3 significant figures.