Complete Guide to Significant Figures Rules
Master all the rules for identifying, counting, and using significant figures correctly
What Are Significant Figures?
Significant figures (also called significant digits) are the meaningful digits in a number that indicate the precision of a measurement or calculation. They tell us how accurately we know a value.
🔬 In Science
Indicate measurement precision and experimental uncertainty
🏭 In Engineering
Ensure calculations don't claim false precision
📊 In Data Analysis
Maintain appropriate precision throughout calculations
Basic Identification Rules
These fundamental rules help you identify which digits in a number are significant:
Non-Zero Digits Rule
All non-zero digits (1, 2, 3, 4, 5, 6, 7, 8, 9) are always significant.
Examples:
- 123 → 3 sig figs (all digits are non-zero)
- 7.89 → 3 sig figs (all digits are non-zero)
- 456.78 → 5 sig figs (all digits are non-zero)
Leading Zeros Rule
Leading zeros (zeros before the first non-zero digit) are never significant. They only indicate the position of the decimal point.
Examples:
- 0.0045 → 2 sig figs (only 4 and 5 count)
- 0.000123 → 3 sig figs (only 1, 2, and 3 count)
- 0.7 → 1 sig fig (only 7 counts)
Trailing Zeros After Decimal Rule
Trailing zeros after the decimal point are significant because they indicate precision.
Examples:
- 1.200 → 4 sig figs (zeros show precision to thousandths)
- 0.0450 → 3 sig figs (4, 5, and trailing 0)
- 7.000 → 4 sig figs (all zeros after decimal count)
Zeros Between Non-Zero Digits Rule
Zeros between non-zero digits are always significant.
Examples:
- 1005 → 4 sig figs (all digits including zeros)
- 3.0078 → 5 sig figs (zeros between 3 and 7, 7 and 8)
- 20.09 → 4 sig figs (zero between 2 and 9)
Trailing Zeros in Whole Numbers Rule
Trailing zeros in whole numbers (without decimal point) are ambiguous and typically not considered significant.
Examples:
- 1200 → 2 sig figs (ambiguous trailing zeros)
- 5000 → 1 sig fig (only the 5 is clearly significant)
- 1200. → 4 sig figs (decimal point clarifies precision)
Clarification: Use a decimal point (1200.) or scientific notation (1.20 × 10³) to indicate that trailing zeros are significant.
Practice with Our Calculator
Test your understanding of these rules with our advanced sig figs calculator. Use the step-by-step mode to see exactly how each rule is applied!