Importance of Units in Measurements

• Units are essential for giving meaning to numbers.
• Contextual example: "4 dollars" vs. "4 murders" highlights the importance of labeling values.

Systems of Units

• English System: Common in the United States but not widely used globally.
• SI System (International System of Units): Preferred for scientific work.
  • Uses base units and prefixes to denote magnitude.

Base and Derived Units

Base Units in SI System

• Length: meter (m)
• Prefixes indicate size:
  • Centi (10^-2): centimeter (cm) is smaller than meter.
  • Kilo (10^3): kilometer (km) is larger than meter.

Derived Units

• Speed: meters per second (m/s)
• Volume: cubic meters (m^3)
• Density: kilograms per cubic meter (kg/m^3)
• Derived units can also use prefixes (e.g., km/s, cm^3).

Properties of Units

• Intensive Properties: Do not depend on the amount of substance.
  • Example: Density.
• Extensive Properties: Depend on the amount of substance.
  • Example: Mass.

Example Problem

• Scenario: Determine if a ring is platinum.
  • Given: Mass = 3.15 g, Volume = 0.233 cm^3, Platinum Density = 21.4 g/cm^3.
  • Method 1: Calculate density of ring and compare.
    • Density = 3.15 g / 0.233 cm^3 = 13.52 g/cm^3.
    • Conclusion: Not platinum (incorrect density).
  • Method 2: Calculate expected mass of platinum and compare.
    • Formula: Density = Mass/Volume, solve for Mass.
    • Expected Mass = 21.4 g/cm^3 * 0.233 cm^3 = 4.99 g.
    • Conclusion: Ring mass (3.15 g) is lower, thus not platinum.

Takeaways

• Multiple valid methods can solve the same problem.
• Important to understand and apply units correctly for accurate measurements and conclusions.