Counting significant figures
- All non-zero digits count: 347 has 3.
- Zeros between non-zero digits count: 4007 has 4.
- Leading zeros never count: 0.0045 has 2.
- Trailing zeros after a decimal point count: 0.00450 has 3, and 2.50 has 3.
- Trailing zeros in a whole number without a decimal point are ambiguous: 1200 could have 2, 3 or 4.
Scientific notation removes the doubt
Write 1200 as 1.2 × 103 for 2 significant figures, or 1.200 × 103 for 4. Every digit shown in the number before × 10 is significant.
Rounding results
- Multiplying and dividing: keep as many significant figures as the least precise value. 4.56 × 1.4 = 6.384, which rounds to 6.4.
- Adding and subtracting: keep as many decimal places as the value with the fewest. 12.11 + 0.3 = 12.41, which rounds to 12.4.
- Round only at the end of a calculation, not at each step.
- Exact numbers, such as counted items or defined conversions, do not limit the result.
Calculators
The Significant Figures Calculator counts and rounds any number. The Scientific Notation Converter and the Engineering Notation Converter write it in either form.
A worked example
A sample has a mass of 12.5 g (3 significant figures) and a volume of 4.2 mL (2 significant figures). Its density is 12.5 ÷ 4.2 = 2.976…, which rounds to 3.0 g/mL: two significant figures, and the zero after the decimal point shows it.
Mixed calculations
Apply the rules step by step but keep the extra digits until the end. For (12.11 + 0.3) × 2.0: the sum is 12.41, good to one decimal place (12.4), and 12.41 × 2.0 = 24.82, which rounds to 25 with two significant figures. Rounding the sum to 12.4 first would also give 24.8 → 25 here, but in longer calculations early rounding adds up.
Rounding a 5
Most courses round a final 5 up: 2.45 becomes 2.5. Some lab and statistics texts round to the even digit instead, so 2.45 becomes 2.4 and 2.55 becomes 2.6, which avoids pushing averages upward. Use whichever your course or journal asks for.