Significant Figures Calculator
Significant Figures Calculator
Related Tools
What are Significant Figures?
Significant figures (sig figs) are the digits in a number that carry meaningful information about its precision. In science and engineering, significant figures indicate how precisely a measurement was made. The more significant figures, the more precise the measurement.
This calculator helps you count significant figures in any number, round numbers to a specific number of sig figs, and perform arithmetic operations while following proper significant figure rules used in chemistry, physics, and other sciences.
Understanding sig figs is essential for lab reports, scientific calculations, and ensuring that your answers reflect the precision of your measurements - not false precision from calculator displays.
Significant Figure Rules
1. Non-Zero Digits
All non-zero digits are always significant.
Example: 1234 has 4 sig figs, 5.67 has 3 sig figs
2. Zeros Between Non-Zero Digits
Zeros between significant digits are always significant (captive zeros).
Example: 1002 has 4 sig figs, 3.04 has 3 sig figs
3. Leading Zeros
Zeros before the first non-zero digit are NOT significant (placeholders only).
Example: 0.0025 has 2 sig figs, 0.00340 has 3 sig figs
4. Trailing Zeros
Trailing zeros after a decimal point are significant. Without a decimal, they may be ambiguous.
Example: 2.50 has 3 sig figs, 1200 has 2-4 sig figs (ambiguous without scientific notation)
Sig Fig Rules for Calculations
Addition & Subtraction
Round the result to the same number of decimal places as the measurement with the fewest decimal places.
Example: 12.52 + 1.3 = 13.8 (round to 1 decimal place)
Multiplication & Division
Round the result to the same number of significant figures as the measurement with the fewest sig figs.
Example: 2.5 × 3.42 = 8.6 (round to 2 sig figs)
Frequently Asked Questions
How do I count significant figures?
Start from the first non-zero digit and count all digits including zeros between significant digits and trailing zeros after a decimal point. Leading zeros don't count. For example, 0.00340 has 3 sig figs (3, 4, and the trailing 0).
Are trailing zeros significant?
It depends on whether there's a decimal point. In 2.50, the trailing zero IS significant (3 sig figs). In 1200, the trailing zeros are ambiguous - use scientific notation (1.2 × 10³ for 2 sig figs, or 1.200 × 10³ for 4 sig figs) to be clear.
Why do sig fig rules differ for addition vs multiplication?
Addition/subtraction deals with absolute precision (how many decimal places), while multiplication/division deals with relative precision (how many sig figs). When adding, you can't gain precision beyond your least precise measurement's decimal place. When multiplying, you can't be more precise than your least precise factor.
When should I use significant figures?
Use sig figs whenever you're working with measured quantities in science, engineering, or statistics. They're essential in chemistry and physics lab work, scientific research papers, engineering calculations, and any situation where measurement precision matters.
Examples
Counting Sig Figs
| Number | Sig Figs |
|---|---|
| 1234 | 4 |
| 0.0045 | 2 |
| 3.00 | 3 |
| 100.0 | 4 |
| 5.20 × 10³ | 3 |
Calculations
Addition: 12.11 + 0.3 + 1.432 = 13.8
(0.3 has 1 decimal place → round to 1 decimal)
Multiplication: 4.56 × 1.4 = 6.4
(1.4 has 2 sig figs → round to 2 sig figs)