Lecture Notes: Interconversion of Prefixed SI Units

Overview

• Discussing a problem involving the conversion of SI units with prefixes, commonly encountered in measurements.
• Three versions of the problem:
  1. Converting quantities and units.
  2. Simple unit conversion.
  3. Reverse calculation (from larger to smaller quantities).

Version 1: Conversion for Multiple Objects

• Example Problem:
  • Object: Pill
  • Measurement: Mass of 900 milligrams
  • Task: Calculate mass for 100 pills and convert to kilograms.

Steps for Conversion

1. Change Quantity:
   • From 1 object (pill) to 100 objects.
2. Change Unit:
   • From milligrams to kilograms.

Detailed Conversion Process

• Step 1: Unit Conversion (Milligrams to Grams to Kilograms)

  • Start with the given measurement: 900 mg.
  • Convert from milligrams to grams:
    • Conversion Factor: 1 mg = 10^-3 grams
    • Set up a conversion factor:
      • 900 mg x (1 g / 10^-3 mg) = grams
  • Convert from grams to kilograms:
    • Conversion Factor: 1 kg = 10^3 grams
    • Set up a conversion factor:
      • Result from grams x (1 kg / 10^3 g) = kilograms
  • Final Result: 900 mg = 9 x 10^-6 kilograms

• Step 2: Multiply for Quantity

  • Calculate mass for 100 pills:
    • 9 x 10^-6 kg per pill x 100 = 9 x 10^-4 kg for 100 pills
  • Report in decimal form: 0.0900 kilograms

Version 2: Simple Unit Conversion

• Involves only converting units without changing quantities.
  • Example: Direct conversion of a given measurement without regard to the number of objects.

Version 3: Reverse Calculation

• Converts from a larger quantity to a smaller quantity.
  • Example: Given 100 pills with a total mass, find the mass of one pill.
  • Reverse steps:
    • Perform unit conversion first.
    • Divide by the number of objects to find the mass of one object.

Additional Tips

• Two-Step Conversion Method:
  • Convert prefixed units to base units (e.g., milligrams to grams), then to target units (e.g., grams to kilograms) for clarity and accuracy.
• Useful when starting out to avoid errors in handling prefixes and unit conversions directly.
• Refer to SI prefixes tables for accurate conversion factors.

Conclusion:

• The lecture covers multiple problem types involving SI unit conversion, offering detailed methods for approaching each problem effectively.