Unit 1.6 – Significant Figures
Physics → Physics → Physical World & Mechanics → Physical World & Mechanics → Physics & Measurement | Author: admin | Feb 28, 2026
Significant Figures
Significant figures (or significant digits) are the digits in a number that carry meaningful information about the precision of a measurement. They help express results accurately without overstating or understating the level of certainty.
Understanding Significant Figures
1. Definition:
Significant figures include all certain digits in a measurement plus one uncertain digit. For example, if a ruler measures 5.23 cm, the digits "5" and "2" are certain, while "3" is an estimate and represents the uncertainty.
Significant figures include all certain digits in a measurement plus one uncertain digit. For example, if a ruler measures 5.23 cm, the digits "5" and "2" are certain, while "3" is an estimate and represents the uncertainty.
2. Rules for Identifying Significant Figures:
- Non-zero digits: All non-zero digits are significant.
- Example: 456 → 3 significant figures.
- Zeroes between non-zero digits: These are significant.
- Example: 4008 → 4 significant figures.
- Leading zeroes: Zeroes to the left of the first non-zero digit are not significant.
- Example: 0.0045 → 2 significant figures.
- Trailing zeroes:
- In a decimal number, trailing zeroes are significant.
- Example: 3.50 → 3 significant figures.
- In a whole number without a decimal point, trailing zeroes may or may not be significant.
- Example: 400 → Ambiguous (could be 1, 2, or 3 significant figures).
- In a decimal number, trailing zeroes are significant.
Rounding Off Numbers
When performing calculations, it’s important to round off numbers to the correct number of significant figures.
Rules for Rounding Off:
- If the digit to the right of the last significant figure is less than 5, leave the last digit unchanged.
- Example: Round 3.42 to 2 significant figures → 3.4.
- If the digit is 5 or greater, increase the last significant digit by 1.
- Example: Round 6.78 to 2 significant figures → 6.8.
Operations with Significant Figures
1. Addition and Subtraction:
The result should have the same number of decimal places as the least precise measurement.
The result should have the same number of decimal places as the least precise measurement.
- Example:
- 12.34 + 1.2 = 13.54 → Rounded to 13.5 (1 decimal place).
2. Multiplication and Division:
The result should have the same number of significant figures as the least precise measurement.
The result should have the same number of significant figures as the least precise measurement.
- Example:
- 2.5 × 3.14 = 7.85 → Rounded to 7.9 (2 significant figures).
Importance of Significant Figures
- Reflects Precision: Significant figures indicate how precisely a measurement has been made.
- Avoids Misleading Results: Overstating precision can lead to incorrect conclusions.
- Standardizes Reporting: Ensures consistency in scientific communication.
Quick Revision Points
- Significant Figures: Include all certain digits plus one uncertain digit.
- Rules: Non-zero digits are significant; zeroes depend on their position.
- Rounding Off: Follow rules based on the digit to the right of the last significant figure.
- Addition/Subtraction: Match the least number of decimal places.
- Multiplication/Division: Match the least number of significant figures.
Previous Year Questions and Answers
Q1: How many significant figures are in the number 0.00450?
A1: The number 0.00450 has 3 significant figures (4, 5, and the trailing zero after the decimal point).
A1: The number 0.00450 has 3 significant figures (4, 5, and the trailing zero after the decimal point).
Q2: Round off 7.896 to 3 significant figures.
A2: The rounded value is 7.90.
A2: The rounded value is 7.90.
Q3: What is the result of 12.34 + 1.234, rounded to the correct number of significant figures?
A3: 12.34 + 1.234 = 13.574 → Rounded to 13.57 (2 decimal places).
A3: 12.34 + 1.234 = 13.574 → Rounded to 13.57 (2 decimal places).
Q4: Multiply 2.5 × 3.14 and round off to the correct number of significant figures.
A4: 2.5 × 3.14 = 7.85 → Rounded to 7.9 (2 significant figures).
A4: 2.5 × 3.14 = 7.85 → Rounded to 7.9 (2 significant figures).
Q5: Why are significant figures important in measurements?
A5: Significant figures reflect the precision of a measurement and ensure that results are not misleading or overstated.
A5: Significant figures reflect the precision of a measurement and ensure that results are not misleading or overstated.
Expected Questions
Q1: How many significant figures are in the number 1002?
A1: The number 1002 has 4 significant figures (all digits are significant).
A1: The number 1002 has 4 significant figures (all digits are significant).
Q2: Round off 5.678 to 2 significant figures.
A2: The rounded value is 5.7.
A2: The rounded value is 5.7.
Q3: Add 4.56 and 2.3, and round off to the correct number of significant figures.
A3: 4.56 + 2.3 = 6.86 → Rounded to 6.9 (1 decimal place).
A3: 4.56 + 2.3 = 6.86 → Rounded to 6.9 (1 decimal place).
Q4: Divide 15.0 by 2.50 and round off to the correct number of significant figures.
A4: 15.0 ÷ 2.50 = 6.00 → Rounded to 6.00 (3 significant figures).
A4: 15.0 ÷ 2.50 = 6.00 → Rounded to 6.00 (3 significant figures).
Q5: What is the significance of trailing zeroes in a decimal number?
A5: Trailing zeroes in a decimal number are significant because they indicate the precision of the measurement.
A5: Trailing zeroes in a decimal number are significant because they indicate the precision of the measurement.