Significant Figures Calculator
Count significant figures in a number or round to a specific number of sig figs.
Results
Examples
Rules for Significant Figures
Always Significant
- • All non-zero digits (1, 2, 3...)
- • Zeros between non-zero digits (102, 5.007)
- • Trailing zeros after decimal point (2.50, 100.0)
Never Significant
- • Leading zeros (0.0045 has 2 SF)
Sometimes Significant
- • Trailing zeros without decimal point (100 could be 1, 2, or 3 SF)
- • Use scientific notation to clarify: 1.00 × 10² has 3 SF
Why Significant Figures Matter
Significant figures indicate the precision of a measurement. When you report 10.0 cm instead of 10 cm, you're communicating that your measurement is precise to the tenths place. This is crucial in scientific work where accuracy and precision must be clearly communicated.
- • Measurements: Show the precision of your instruments
- • Calculations: Results can't be more precise than inputs
- • Communication: Prevents false precision claims
Sig Figs in Calculations
When performing calculations, the number of significant figures in your answer depends on the operation. These rules ensure that your results don't overstate the precision of your original measurements.
Multiplication & Division
Round result to the fewest sig figs of any input.
4.56 × 1.4 = 6.384 → 6.4 (2 SF)
12.34 ÷ 3.0 = 4.113... → 4.1 (2 SF)
Addition & Subtraction
Round result to the fewest decimal places of any input.
12.34 + 1.1 = 13.44 → 13.4 (1 decimal place)
100 + 0.1 = 100.1 → 100 (no decimal places)
Significant Figures in Scientific Notation
Scientific notation is the best way to eliminate ambiguity about trailing zeros. The coefficient (the number before × 10ⁿ) shows exactly how many digits are significant.
| Standard Form | Scientific Notation | Sig Figs |
|---|---|---|
| 1500 | 1.5 × 10³ | 2 |
| 1500 | 1.50 × 10³ | 3 |
| 1500 | 1.500 × 10³ | 4 |
| 0.00230 | 2.30 × 10⁻³ | 3 |
| 602,200,000,000,000,000,000,000 | 6.022 × 10²³ | 4 |
Scientific notation removes all trailing-zero ambiguity. This is why scientists use it universally — writing 1.500 × 10³ unambiguously communicates exactly four significant figures.
Step-by-Step: Rounding to Sig Figs
Example 1: Round 0.004567 to 2 sig figs
- Find the first significant digit: 4 (leading zeros don't count)
- Count 2 sig figs from there: 4 and 5
- Look at the next digit: 6 ≥ 5, so round up
- Result: 0.0046
Example 2: Round 149,800 to 3 sig figs
- First three sig figs: 1, 4, 9
- Next digit is 8 ≥ 5, so round up 9 to 10 → carry the 1
- Result: 150,000
- For clarity, write as 1.50 × 10⁵ (3 sig figs explicitly)
Example 3: Round 3.14159 to 4 sig figs
- First four sig figs: 3, 1, 4, 1
- Next digit is 5 ≥ 5, so round up
- Result: 3.142