Significant Figures Calculator
Count the number of significant figures in any number and see which digits are significant. See also Rounding Calculator and Scientific Notation Calculator.
How to Count Significant Figures
Significant figures (sig figs) are the meaningful digits in a number that contribute to its precision. To count them: (1) All non-zero digits are significant. (2) Zeros between non-zero digits are significant. (3) Leading zeros are never significant. (4) Trailing zeros after a decimal point are significant. (5) Trailing zeros in a whole number without a decimal point are ambiguous.
Significant Figures Rules
Rule 1: Non-zero digits are always significant
Rule 2: Zeros between non-zero digits are significant
Rule 3: Leading zeros are NOT significant
Rule 4: Trailing zeros after decimal ARE significant
Rule 5: Trailing zeros in integers are ambiguous
Example
Number: 0.00340
Leading zeros (0.00): NOT significant
Digits 3, 4: significant
Trailing zero after decimal (0): significant
Total significant figures: 3
Scientific notation: 3.40 × 10⁻³
Frequently Asked Questions
Why are leading zeros not significant?
Leading zeros only serve as placeholders to show the position of the decimal point. They do not reflect the precision of the measurement. For example, 0.005 has 1 sig fig — the 5.
Are trailing zeros significant in 1500?
It depends on context. Without a decimal point, 1500 could have 2, 3, or 4 sig figs. Writing it as 1500. (with a decimal) or 1.500 × 10³ makes the precision clear.
How do sig figs apply to calculations?
For multiplication and division, the result should have the same number of sig figs as the input with the fewest sig figs. For addition and subtraction, the result should match the least precise decimal place.
Is the number 0 significant?
The number 0 by itself has 1 significant figure. Zeros can be significant depending on their position — between non-zero digits or trailing after a decimal point.
Solved Examples — Significant Figures
Example: How many significant figures in 0.004070?
Solution:
Step 1: Leading zeros (0.00) — NOT significant
Step 2: 4 — significant (non-zero digit)
Step 3: 0 (between 4 and 7) — significant (between non-zero digits)
Step 4: 7 — significant (non-zero digit)
Step 5: 0 (trailing after decimal) — significant
Answer: 4 significant figures
Example: Round 0.08726 to 3 significant figures
Solution:
Step 1: Leading zeros don't count. Start counting from 8.
Step 2: First 3 sig figs: 8, 7, 2
Step 3: Next digit is 6 (≥ 5), so round up: 2 → 3
Answer: 0.0873
Example: Multiply 4.56 × 1.4 and report with correct sig figs
Solution:
Step 1: 4.56 has 3 sig figs, 1.4 has 2 sig figs
Step 2: Product = 4.56 × 1.4 = 6.384
Step 3: Result should have 2 sig figs (minimum of inputs)
Step 4: Round 6.384 to 2 sig figs = 6.4
Answer: 6.4
Practice Questions
Try these on your own:
- How many sig figs in 50,600? (Answer: 3 — trailing zeros without decimal are ambiguous, typically 3)
- How many sig figs in 8.0200? (Answer: 5)
- Round 1,476 to 2 significant figures (Answer: 1,500)
- Add 12.52 + 3.7 with correct sig figs (Answer: 16.2)
- How many sig figs in 1.00 × 10⁴? (Answer: 3)
- Divide 84.56 ÷ 3.2 with correct sig figs (Answer: 26)
Common Mistakes to Avoid
The most common mistake is treating all zeros the same way. Leading zeros are NEVER significant (0.003 has 1 sig fig), but trailing zeros after a decimal point ARE significant (3.00 has 3 sig figs). Another frequent error is using the wrong rule for calculations: multiplication/division uses the fewest significant figures, while addition/subtraction uses the fewest decimal places — these are different rules! Students also forget that exact numbers (like counting 12 eggs or conversion factors like 1 km = 1000 m) have infinite significant figures and don't limit your answer. When in doubt about trailing zeros in whole numbers like 200, use scientific notation (2.00 × 10² for 3 sig figs) to make your precision clear.
Key Takeaways
- Non-zero digits are always significant. Zeros between non-zero digits are always significant.
- Leading zeros are never significant — they are just placeholders.
- Trailing zeros after a decimal point are significant (they show precision).
- For multiplication/division: answer has the same sig figs as the input with the fewest.
- For addition/subtraction: answer has the same decimal places as the input with the fewest.
- Use scientific notation to remove ambiguity in whole numbers (2.0 × 10³ = 2 sig figs).