Lecture Notes: Dimensional Analysis and Conversion Calculations

Introduction

Definition: A method to convert between units ensuring units cancel out appropriately.
Process: Start with a given value, use conversion factors, and perform calculations so units cancel.

Common Metric Conversions:
- Many involve factors of 1000, assign 1000 to the smaller unit.
- Example: 1000 milliliters (mL) in a liter (L).
Examples:
- Convert 83 cm to meters (83 cm ÷ 100 = 0.83 m).
- Convert 4.59 L to mL (4.59 L × 1000 = 4590 mL).
- Convert 78.24 mg to grams (78.24 mg ÷ 1000 = 0.07824 g or 7.824 × 10^-2 g in scientific notation).

Fahrenheit to Celsius:
- Formula: ( C = (F - 32) \times \frac{5}{9} )
- Example: 172.9°F to Celsius gives 78.3°C.
Celsius to Kelvin:
- Formula: Add 273.15 to the Celsius temperature.
- Example: 212 K to Celsius results in -61.15°C.

Steps:
- Identify starting and ending units.
- Prepare a list of conversion factors.
- Arrange units to ensure cancellation.
- Decide on multiplication or division based on the position of numbers (top or bottom).

Volume Conversion:
- 12 oz to mL using the factor 29.6 mL per fluid oz: 12 × 29.6 = 355 mL
Volume in Medicine:
- Convert 5 microliters to mL: Use multiple conversion factors for microliters to liters, then liters to mL (final result: 5.0 × 10^-3 mL).
Mass Conversion:
- Convert long tons (2240 lbs) to kilograms using 1 kg = 2.2046 lbs: Result is 1020 kg.
Area and Volume:
- Convert area in miles squared to km squared, and volume in cubic miles to cubic km using appropriate squared or cubed conversion factors.

Definition: Density = Mass/Volume
Using Density as Conversion Factor:
- Density of mercury used to convert volumes to mass.
- Example: Convert 6.0 cm³ mercury to grams (density = 13.5939 g/cm³): 6.0 × 13.5939 = 81.6 g
Reverse Conversion:
- Given mass to find volume using inverse density.