Significant Figures and Rounding Rules for Accurate Results
Significant figures communicate the precision of a measurement. Incorrect rounding can introduce errors that compound through calculations. This guide covers the rules and common mistakes.
Key Takeaways
- Significant figures (sig figs) are the meaningful digits in a number that contribute to its precision.
- Use scientific notation to remove ambiguity: `1.500 × 10³` clearly has 4 sig figs.
- If the digit after your last significant figure is 5 or greater, round up.
- Round the result to the fewest decimal places in any operand.
- Rounding intermediate results (round only the final answer to avoid compounding errors)
What Are Significant Figures
Significant figures (sig figs) are the meaningful digits in a number that contribute to its precision. They tell you how accurately a measurement was made.
Counting Rules
| Rule | Example | Sig Figs |
|---|---|---|
| Non-zero digits always count | 3.456 | 4 |
| Zeros between non-zeros count | 1,005 | 4 |
| Leading zeros do NOT count | 0.0042 | 2 |
| Trailing zeros after decimal count | 2.300 | 4 |
| Trailing zeros without decimal are ambiguous | 1,500 | 2, 3, or 4 |
Use scientific notation to remove ambiguity: 1.500 × 10³ clearly has 4 sig figs.
Rounding Rules
Standard Rounding
If the digit after your last significant figure is 5 or greater, round up. If less than 5, round down. Example: 3.456 rounded to 3 sig figs = 3.46.
Banker's Rounding (Round Half to Even)
When the digit is exactly 5 with no trailing digits, round to the nearest even number. This reduces systematic upward bias:
- 2.35 → 2.4 (round up)
- 2.45 → 2.4 (round down to even)
Calculation Rules
Addition / Subtraction
Round the result to the fewest decimal places in any operand.
12.3 + 1.456 = 13.756 → 13.8 (1 decimal place)
Multiplication / Division
Round the result to the fewest significant figures in any operand.
4.56 × 1.4 = 6.384 → 6.4 (2 sig figs)
Common Mistakes
- Rounding intermediate results (round only the final answer to avoid compounding errors)
- Reporting calculator outputs at full precision when input data has only 2-3 sig figs
- Treating exact numbers (like counting 12 eggs) as having limited precision — exact values have infinite sig figs