Significant Figures Rules

Master the complete rules for counting and calculating with significant figures.

What Are Significant Figures?

Significant figures are the digits in a number that carry meaningful information about its precision.

Key Concept: Sig figs communicate measurement precision. More sig figs = more precise measurement.

The 5 Rules for Counting Significant Figures

Non-Zero Digits

All non-zero digits (1-9) are ALWAYS significant

123 → 3 SF45.67 → 4 SF7 → 1 SF

Zeros Between Non-Zero Digits

Zeros that appear between non-zero digits ARE significant

101 → 3 SF5.007 → 4 SF1002 → 4 SF

Leading Zeros

Leading zeros (before the first non-zero digit) are NOT significant

0.005 → 1 SF0.0420 → 3 SF0.00001 → 1 SF

Trailing Zeros After Decimal

Trailing zeros after a decimal point ARE significant

2.50 → 3 SF100.0 → 4 SF3.0 → 2 SF

Trailing Zeros Without Decimal

Trailing zeros in a whole number without decimal are AMBIGUOUS

100 → 1 SF (ambiguous)1000 → 1 SF (ambiguous)Use 1.00×10² for clarity

Rules for Math Operations

× ÷ Multiplication & Division

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

12.5 × 3.2 = 40.0 → 40

12.5 (3 SF) × 3.2 (2 SF) = 2 SF

+ − Addition & Subtraction

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

12.52 + 3.1 = 15.62 → 15.6

12.52 (2 DP) + 3.1 (1 DP) = 1 DP

Scientific Notation and Sig Figs

Eliminate ambiguity with scientific notation

Scientific notation is useful for clearly showing significant figures, especially when trailing zeros would be ambiguous.

300

Ambiguous (1, 2, or 3 SF?)

3.0 × 10²

Clear: 2 sig figs

3.00 × 10²

Clear: 3 sig figs

Common Mistakes to Avoid

Counting leading zeros as significant

0.005 has 1 SF, not 4.

Assuming trailing zeros are significant

100 has 1 SF by default.

Using the wrong rule for operations

Multiplication uses sig figs count. Addition uses decimal places.

Rounding intermediate steps

Keep extra digits during calculation. Only round the final answer.

Frequently Asked Questions

What are significant figures?

Significant figures (sig figs) are the digits in a number that carry meaningful information about its precision. They indicate how precisely a measurement was made.

Why are significant figures important in chemistry?

Sig figs prevent you from claiming more precision than your measurements actually have. Proper sig fig usage ensures your calculated results reflect the actual precision of your data.

How many sig figs in 100?

100 has only 1 significant figure by default because trailing zeros without a decimal point are ambiguous. To show 3 sig figs, write '100.' with a decimal point, or use scientific notation: 1.00 × 10².

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.

What's the difference between accuracy and precision?

Accuracy is how close a measurement is to the true value. Precision is how reproducible measurements are. Significant figures relate to precision.

Do exact numbers have significant figures?

Exact numbers (like counting 12 eggs, or defined values like 1 inch = 2.54 cm exactly) have infinite significant figures.

Ready to Practice?

Use our free sig fig calculator to apply these rules automatically.

Sig Fig Calculator Sig Fig Counter Rounding Tool