SigFigCalculator

Sig Fig Calculator (with Steps)

Instantly count significant figures and perform mixed operations (+, −, ×, ÷) with automatic rule application. Unlike basic calculators, our sig fig calculator shows you the why behind every step.

📖 How to Use This Sig Fig Calculator
1
Enter your expression in the input box using the keypad or keyboard (e.g., 12.5 * 3.2)
2
Click "Solve" or press Enter to calculate
3
View results: Exact result, rounded result (with correct sig figs), and scientific notation
4
Expand "Step by Step" to see how sig figs were identified and which rules were applied
5
Optional: Select a specific number of sig figs (1-5) to round your result differently
6
Copy & Share: Click copy buttons to copy results, or share the calculation link
💡 Pro Tip: Use * for multiplication, / for division, ^ for exponents, and 3e2 for scientific notation (3×10²).

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How to Identify Significant Figures

Mastering the rules for calculating significant figures is essential for chemistry and physics. Our sig fig calculator applies these rules automatically, but understanding them helps you verify your work.

The 5 Golden Rules for Significant Digits
1
Non-zero digits are ALWAYS significant
Example: 1234 has 4 sig figs, 56.78 has 4 sig figs
2
Zeros BETWEEN non-zero digits are significant
Example: 101 has 3 sig figs, 5.007 has 4 sig figs
3
Leading zeros are NEVER significant
Example: 0.005 has 1 sig fig, 0.0420 has 3 sig figs
4
Trailing zeros AFTER a decimal point ARE significant
Example: 2.50 has 3 sig figs, 3.0 has 2 sig figs
5
Trailing zeros WITHOUT a decimal point are AMBIGUOUS
Example: 100 could be 1, 2, or 3 sig figs — use scientific notation to be clear!

Common Tricky Examples

These are the numbers that trip up most students. Use our sig fig calculator to verify your answers, and study these examples to avoid common mistakes on your chemistry homework.

NumberSig FigsExplanation
1001Trailing zeros without decimal point are NOT significant. This is the classic trap!
10001Same rule: trailing zeros without decimal don't count. Write 1000. for 4 sig figs.
100.3The decimal point makes ALL digits significant, including trailing zeros.
3.02Trailing zero AFTER decimal point IS significant. The .0 matters!
2.02Same rule: 2.0 has 2 sig figs because trailing zeros after decimal count.
5.02The zero after the decimal indicates measured precision - it's significant.
0.0050204Leading zeros don't count (0.00), but trailing zeros after decimal do (5020).
1.00 × 10³3Scientific notation makes sig figs unambiguous. The coefficient shows 3 sig figs.

Operations with Significant Figures

The rules for calculating significant figures differ between multiplication/division and addition/subtraction. Our sig fig calculator handles both automatically, showing you which rule applies at each step.

× ÷ Multiplication & Division Rule

The result must have the same number of significant figures as the measurement with the fewest sig figs.

2.0 × 3.15 = ?
2.0 has 2 sig figs, 3.15 has 3 sig figs
Calculator shows: 6.3
Answer: 6.3 (2 sig figs)
+ − Addition & Subtraction Rule

The result must have the same number of decimal places as the measurement with the fewest decimal places.

12.52 + 1.3 = ?
12.52 has 2 decimal places, 1.3 has 1 decimal place
Calculator shows: 13.82
Answer: 13.8 (1 decimal place)

Mixed Operations (PEMDAS)

For complex expressions with multiple operations, follow order of operations (PEMDAS). Keep extra digits in intermediate steps and only round the final answer. Our sig fig calculator handles this automatically — try entering 12.5 * 3.2 + 1.5 to see it in action!

How to Round Significant Figures

After calculating significant figures, you need to round correctly. The rounding rules for chemistry are straightforward, and our sig fig calculator applies them automatically.

Standard
If the digit to drop is 5 or greater, round up
Example: 2.35 → 2.4 (rounding to 2 sig figs)
Standard
If the digit to drop is less than 5, round down
Example: 2.34 → 2.3 (rounding to 2 sig figs)
Advanced
Banker's Rounding (Round Half to Even)
When exactly 5, round to nearest even number. Used in some advanced contexts, but most chemistry classes use standard rounding.

Scientific Notation and Sig Figs

Scientific notation eliminates ambiguity in significant figures. When you're unsure how many sig figs a number like "300" has, scientific notation makes it crystal clear.

300
Ambiguous (1, 2, or 3 SF?)
3.0 × 10²
Clear: 2 sig figs
3.00 × 10²
Clear: 3 sig figs

Tip: Enter scientific notation in our sig fig calculator using E-notation: type 3e2 for 3 × 10² or 5.5e-3 for 5.5 × 10⁻³.

Frequently Asked Questions

How many sig figs in 100?
100 has only 1 significant figure. The trailing zeros are NOT significant because there's no decimal point. This is one of the most common mistakes! To show 3 sig figs, write "100." with a decimal point, or use scientific notation: 1.00 × 10².
How many significant figures in 1000?
1000 has 1 significant figure by default. The three trailing zeros are placeholders, not measured values. To indicate more precision, use: 1000. (4 sig figs), 1.0 × 10³ (2 sig figs), or 1.000 × 10³ (4 sig figs).
How many sig figs in 3.0?
3.0 has 2 significant figures. The trailing zero after the decimal point IS significant because it indicates the measurement was precise to the tenths place. This is different from just writing "3" which has only 1 sig fig.
Are exact numbers significant?
Exact numbers (like counting 12 eggs, or defined values like 1 inch = 2.54 cm exactly) have infinite significant figures. They don't limit the precision of your calculation because they're not measured values.
Do leading zeros ever count as significant?
No, leading zeros NEVER count as significant figures. They're just placeholders to show the decimal position. For example, 0.005 has only 1 sig fig (the 5). The zeros before it just indicate magnitude.
Why do we need significant figures?
Significant figures communicate measurement precision. When you measure something as 2.5 cm, you're saying it's between 2.45 and 2.55 cm. Reporting a calculated result as 2.5000000 cm would falsely imply more precision than your measurement actually had.
How do I use this sig fig calculator?
Simply type your expression in the input box (e.g., 12.5 * 3.2) and click 'Solve'. The calculator will show you the exact result, the rounded result with correct sig figs, and a step-by-step explanation. You can use +, -, *, / for operations and parentheses for grouping.
Why is my answer showing in scientific notation?
When a number has trailing zeros that would be ambiguous (like 40 with 2 sig figs), we display it in scientific notation (4e+1) to clearly show the precision. This is the scientifically correct way to express such numbers.
Can I enter scientific notation?
Yes! Use E-notation: type 3e2 for 3×10², or 5.5e-3 for 5.5×10⁻³. This is especially useful when you need to specify exact sig figs for numbers like 300 (ambiguous) vs 3.00e2 (3 sig figs).
What operations does this calculator support?
Our sig fig calculator supports addition (+), subtraction (-), multiplication (*), division (/), exponents (^), parentheses for grouping, and functions like log() and ln(). It automatically applies the correct sig fig rules for each operation type.

Ready to Calculate?

Use our free sig fig calculator above to solve any significant figures problem. See step-by-step solutions and never second-guess your chemistry homework again!

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