Significant figures are a critical concept in scientific measurement and mathematical precision. They represent the digits that carry meaningful information about the precision of a measurement. Understanding how to identify, count, and use significant figures ensures accurate scientific communication and proper rounding of calculations.
What Are Significant Figures?
Significant figures are all the digits in a number that are known with certainty, plus one estimated digit. They tell us how precisely a value has been measured or calculated.
Measurement: 5.67 cm has 3 significant figures
Measurement: 0.0045 km has 2 significant figures
Measurement: 1,200 m has 2, 3, or 4 significant figures (ambiguous)
Rules for Counting Significant Figures
Rule 1: Non-zero digits are always significant
23.56 has 4 significant figures
405 has 3 significant figures
Rule 2: Zeros between non-zero digits are significant
3.05 has 3 significant figures
1002 has 4 significant figures
Rule 3: Leading zeros are not significant
0.0045 has 2 significant figures (4 and 5 are significant)
0.00002 has 1 significant figure
Rule 4: Trailing zeros after a decimal point are significant
2.50 has 3 significant figures
0.500 has 3 significant figures
Rule 5: Trailing zeros in a whole number without a decimal point are ambiguous
1200 could have 2, 3, or 4 significant figures
Write as 1.2 ร 10ยณ (2 sig figs) or 1.20 ร 10ยณ (3 sig figs) to clarify
Significant Figures Examples
| Number | Sig Figs | Explanation |
|---|---|---|
| 45.3 | 3 | All non-zero digits |
| 0.0067 | 2 | Leading zeros don't count |
| 5.00 | 3 | Trailing zeros after decimal count |
| 1,050 | 3 | Trailing zero before decimal, ambiguous |
| 6.02 ร 10ยฒยณ | 3 | Count digits in coefficient |
| 3.0 | 2 | Zero after decimal counts |
| 0.200 | 3 | All three digits are significant |
Rules for Calculations
Addition and Subtraction: The answer has the same number of decimal places as the measurement with the fewest decimal places.
23.5 cm + 0.67 cm = 24.17 cm โ round to 24.2 cm
(23.5 has 1 decimal place)
Multiplication and Division: The answer has the same number of significant figures as the measurement with the fewest significant figures.
2.5 cm ร 3.42 cm = 8.55 cmยฒ โ round to 8.5 cmยฒ
(2.5 has 2 sig figs, 3.42 has 3 sig figs)
Worked Examples
Example 1: Addition
14.5 g + 23.67 g + 8.2 g = ?
46.37 g โ round to 46.4 g
(14.5 and 8.2 have 1 decimal place)
Example 2: Multiplication
5.0 ร 2.45 = ?
12.25 โ round to 12
(5.0 has 2 sig figs, 2.45 has 3 sig figs)
Example 3: Mixed Operations
(23.5 ร 4.2) รท 3.67 = ?
98.7 รท 3.67 = 26.9
(23.5 ร 4.2 gives 2 sig figs result)
Rounding with Significant Figures
When rounding to a specific number of significant figures:
- Count from the left, starting with non-zero digit
- Keep all digits up to your target count
- Look at the next digit
- Round up if it's 5 or greater; round down if it's less than 5
Example: Round 45,678 to 3 significant figures
45,678 โ 45,700 (the 6 tells us to round up the 7)
Real-World Significance
| Measurement | Sig Figs | Implication |
|---|---|---|
| 5.0 g | 2 | Known to nearest 0.1 g |
| 5.00 g | 3 | Known to nearest 0.01 g |
| 5.000 g | 4 | Known to nearest 0.001 g |
| 5 g | 1 | Known to nearest 1 g |
Scientific Notation and Significant Figures
Scientific notation makes it easier to show significant figures:
1,200 could be 1.2 ร 10ยณ (2 sig figs) or 1.200 ร 10ยณ (4 sig figs)
0.0045 = 4.5 ร 10โปยณ (2 sig figs, now clear)
Why Significant Figures Matter
Significant figures tell anyone reading your measurement or calculation how certain you are. A distance recorded as 10 m suggests a rough measurement, while 10.0 m indicates much greater precision. In scientific work, this distinction is crucial for evaluating data quality and drawing valid conclusions.
Use our Significant Figures Calculator to instantly count sig figs and round measurements.