Count, identify, and calculate with significant figures instantly.
Pop quiz: How many significant figures are in 0.00340? If you just stared at the screen trying to remember whether those leading zeros count… you’re not alone.
This calculator thinks for you. Drop in any number and instantly see which digits are significant, which rules apply, and why. Need calculations? We handle sig fig rules for +, −, ×, and ÷ automatically.
📝 Enter Your Number
Significant Figures Highlighted
3
significant figures
Scientific Notation
3.40 × 10-3
📋 Rules Applied to This Number
✂️ Round to Specific Significant Figures
🧮 Calculation with Significant Figures
4 sig figs
2 sig figs
12.34 + 5.6 = 17.94
Raw Result
17.94
Proper Sig Figs
17.9
Sig Figs in Result
3
Rule Applied: For addition/subtraction, result has the same decimal places as the least precise number (5.6 has 1 decimal place).
📖 How to Use This Calculator
1
Enter Number
Type any number, decimal, or scientific notation
2
See Sig Figs
View highlighted significant digits and count
3
Learn Rules
Understand which rules apply to your number
4
Round or Calculate
Round to specific sig figs or perform calculations
📐 Significant Figures Rules
1️⃣ Non-Zero Digits
All non-zero digits are always significant.
123 → 3 sig figs
45.67 → 4 sig figs
2️⃣ Captive Zeros
Zeros between non-zero digits are always significant.
101 → 3 sig figs
40.05 → 4 sig figs
3️⃣ Leading Zeros
Zeros before the first non-zero digit are never significant.
0.0045 → 2 sig figs
0.123 → 3 sig figs
4️⃣ Trailing Zeros (After Decimal)
Trailing zeros after a decimal point are always significant.
2.00 → 3 sig figs
0.0340 → 3 sig figs
5️⃣ Trailing Zeros (Whole Numbers)
Trailing zeros in whole numbers without decimal are ambiguous.
1200 → 2, 3, or 4?
1200. → 4 sig figs (decimal shown)
🧮 Calculation Rules
+/−: Match fewest decimal places
×/÷: Match fewest sig figs
12.11 + 0.3 = 12.4
4.56 × 1.2 = 5.5
📊 Quick Reference Examples
| Number | Sig Figs | Explanation |
|---|---|---|
1234 | 4 | All non-zero digits count |
1234.0 | 5 | Trailing zero after decimal counts |
0.0234 | 3 | Leading zeros don’t count |
0.02340 | 4 | Trailing zero after decimal counts |
1000 | 1-4 | Ambiguous without context |
1000. | 4 | Decimal indicates all zeros count |
1.000 × 10³ | 4 | Scientific notation is clear |
10.0 | 3 | Middle and trailing zeros count |
0.00100 | 3 | Only 1, 0, 0 (after decimal) count |
2.07 | 3 | Captive zero counts |
🎯 Exact Numbers
Some numbers have unlimited significant figures:
- Counting numbers (12 apples = exact)
- Defined values (1 inch = 2.54 cm)
- Formula coefficients
📏 Measurement Precision
Significant figures reflect your measuring tool’s precision:
- Ruler to mm → 3 sig figs typical
- Digital scale → check display digits
- More sig figs = more precise
⚠️ Common Mistakes
- Counting leading zeros as significant
- Forgetting trailing zeros after decimal
- Using sig fig rules for +/− (use decimal places!)
- Rounding intermediate steps (only round final answer)
❓ Frequently Asked Questions
How do I count significant figures?
Follow these rules: (1) All non-zero digits are significant. (2) Zeros between non-zero digits are significant. (3) Leading zeros are NOT significant. (4) Trailing zeros after a decimal point ARE significant. (5) Trailing zeros in whole numbers without a decimal are ambiguous.
How many significant figures are in 0.00250?
There are 3 significant figures: 2, 5, and the final 0. The leading zeros (0.00) are not significant — they’re placeholders. The trailing zero after 5 is significant because it comes after the decimal point.
Do leading zeros count as significant figures?
No, leading zeros are never significant. They’re placeholders that show the decimal point’s position. In 0.0045, only the 4 and 5 are significant (2 sig figs).
Do trailing zeros count as significant figures?
It depends. Trailing zeros AFTER a decimal point always count (12.00 has 4 sig figs). Trailing zeros in whole numbers WITHOUT a decimal point are ambiguous (1200 could be 2, 3, or 4 sig figs).
How do sig figs work for addition and subtraction?
For addition and subtraction, the answer should have the same number of DECIMAL PLACES as the number with the fewest decimal places. Example: 12.11 + 0.3 = 12.4 (not 12.41, because 0.3 has only 1 decimal place).
How do sig figs work for multiplication and division?
For multiplication and division, the answer should have the same number of SIGNIFICANT FIGURES as the input with the fewest sig figs. Example: 4.56 × 1.2 = 5.5 (not 5.472, because 1.2 has only 2 sig figs).
What’s the difference between 100 and 100.0?
100 (without decimal) could have 1, 2, or 3 sig figs — it’s ambiguous. 100.0 (with decimal and trailing zero) clearly has 4 significant figures. The decimal point and trailing zero indicate precision.
How do I show exact sig figs in ambiguous numbers?
Use scientific notation. Instead of 1200, write 1.2 × 10³ (2 sig figs), 1.20 × 10³ (3 sig figs), or 1.200 × 10³ (4 sig figs). This removes all ambiguity.
What are exact numbers in sig fig calculations?
Exact numbers have unlimited (infinite) significant figures and don’t limit your answer’s precision. Examples: counting numbers (12 eggs), defined conversions (1 inch = 2.54 cm exactly), and formula coefficients.
How do I round to a specific number of significant figures?
Count from the first significant digit to the position you want. Look at the next digit: if it’s 5 or greater, round up; if less than 5, round down. Example: 12.346 rounded to 3 sig figs = 12.3 (the 4 causes no rounding change).