Complete Notes on Significant Figures
Why Significant Figures are Important
Significant figures ensure accurate reporting of measurements in experiments and numerical calculations, maintaining precision in physics problems. They are critical for CBSE practical exams, NEET, and JEE, especially in rounding off results.
1. Definition
Significant figures are the digits in a number that contribute to its precision, including all certain digits and one uncertain digit.
2. Key Rules for Significant Figures
Instead of formulas, significant figures rely on rules for counting and performing calculations. Below are the key rules:
- Counting Significant Figures:
- All non-zero digits are significant (e.g., 123 has 3 significant figures).
- Zeros between non-zero digits are significant (e.g., 1002 has 4 significant figures).
- Leading zeros are not significant (e.g., 0.0025 has 2 significant figures).
- Trailing zeros are significant only if the number has a decimal point (e.g., 250.0 has 4 significant figures, but 250 has 2).
- Exact numbers (e.g., counts like 5 apples) have infinite significant figures.
- Arithmetic Rules:
- Addition/Subtraction: Result has the same number of decimal places as the number with the fewest decimal places (e.g., 12.34 + 5.6 = 17.94 → 17.9).
- Multiplication/Division: Result has the same number of significant figures as the number with the fewest significant figures (e.g., 2.5 × 3.20 = 8.0).
- Rounding: Round to the required significant figures, using the next digit to decide (e.g., 5.567 to 3 significant figures → 5.57).
Note: Significant figures are dimensionless and unitless, as they describe measurement precision, not a physical quantity.
3. Real-Life Example
- Lab Measurements: In a physics experiment, a student measures a length as 2.50 cm (3 significant figures) and a mass as 15.0 g (3 significant figures). When calculating density (mass/volume), the result is reported with 3 significant figures to maintain precision.
4. Common Exam Questions and Answers
Answer:
- Leading zeros (0.00) are not significant.
- Digits 2 and 5 are significant.
- Trailing zero after the decimal (0) is significant.
- Total: 3 significant figures.
Answer:
- Addition: 12.34 (2 decimal places) + 5.6 (1 decimal place) = 17.94. Round to 1 decimal place (fewest): 17.9.
- Multiplication: 17.9 (3 significant figures) × 2.5 (2 significant figures) = 44.75. Round to 2 significant figures: 45.
Answer: Significant figures ensure accuracy and precision in measurements, preventing overstatement of results beyond the instrument’s capability. For example, a ruler with 1 mm precision cannot report a length as 2.3456 cm.
5. Diagram/Table
The table below summarizes the rules for counting significant figures, serving as a visual reference:
| Rule | Example | Significant Figures |
|---|---|---|
| Non-zero digits are significant | 123.4 | 4 |
| Zeros between non-zero digits are significant | 1002 | 4 |
| Leading zeros are not significant | 0.0025 | 2 |
| Trailing zeros with a decimal point are significant | 250.0 | 4 |
6. Quick Tips/Tricks
- Counting Trick: Ignore leading zeros, count all other digits, and check trailing zeros for a decimal point.
- Addition/Subtraction: Focus on decimal places, not significant figures, for the final result.
- Multiplication/Division: Use the number with the fewest significant figures to determine the result’s precision.
- NEET/JEE Hack: Practice rounding numerical answers to match the significant figures of the least precise measurement in the problem.
- Memorization: “Significant” means digits that matter—skip leading zeros, keep trailing zeros with decimals.
Note: Significant figures are crucial for maintaining precision in physics calculations and experiments, ensuring results reflect the accuracy of measurements.