Lecture on Significant Figures in Measurements

Introduction

Significant figures are crucial in measurements, especially when performing arithmetic operations.
The rules for significant figures differ when multiplying/dividing versus adding/subtracting.

Rule: The result can only have as many significant digits as the measurement with the smallest number of significant digits.
- Example:
  - Calculation: 2.00 x 3.5
  - Significant digits:
    - 2.00 has 3 significant figures
    - 3.5 has 2 significant figures
  - Result: 7.0 (limited to 2 significant digits)

Difference: Focus on decimal places, not significant figures.
Rule: The result should have as many decimal places as the least precise number in terms of decimal places.
- Example 1:
  - Calculation: 1.26 + 2.3
  - Decimal places to consider:
    - 1.26 has 2 decimal places
    - 2.3 has 1 decimal place
  - Result: 3.7 (rounded to 1 decimal place)
- Example 2:
  - Calculation: 1.26 + 102.3
  - Result: 103.6 (rounded to 1 decimal place)

Scenario: Stacking blocks measured with different precision.
- Block 1: 2.09 meters (nearest cm)
- Block 2: 1.901 meters (nearest mm)
Calculation: 2.09 + 1.901 = 3.991
Adjustment: Round to the least precise measurement (nearest cm): 3.99 meters

Example: Building and radio tower measurements
- Building: 350 feet (nearest 10 feet)
  - Represent as: 3.5 x 10² feet
- Tower: 8 feet (nearest foot)
Calculation and Precision:
- Sum: 350 + 8 = 358 feet
- Adjust: Round to nearest 10 feet: 360 feet
- Possible representations: use a line over the last significant digit or scientific notation (3.6 x 10² feet)

Understanding significant figures ensures accurate representation of measurement precision in calculations.
Different rules apply for multiplication/division versus addition/subtraction.