Overview
This lecture explains how to solve multi-step unit conversion problems, ensuring all unwanted units cancel, and only the desired unit remains at the end.
Multi-Step Unit Conversions
- Multi-step conversions require using several conversion factors sequentially to reach the desired unit.
- Always write out the units with each step to track cancellations and avoid mistakes.
- For each step, place the unit to be canceled opposite (top/bottom) so it divides out.
- You can find intermediate answers at each step or string all conversion factors together for a one-step calculation.
Example 1: Converting Hours to Seconds
- Start with 4 hours.
- Convert hours to minutes: multiply by 60 minutes/1 hour (4 × 60 = 240 minutes).
- Convert minutes to seconds: multiply by 60 seconds/1 minute (240 × 60 = 14,400 seconds).
- Alternatively, multiply all together: 4 × 60 × 60 = 14,400 seconds.
Example 2: Converting Inches to Miles
- Start with 152,000 inches.
- Convert inches to feet: multiply by 1 foot/12 inches.
- Convert feet to miles: multiply by 1 mile/5,280 feet.
- Calculation: 152,000 × 1/12 × 1/5,280 = 2.4 miles.
Example 3: Tablespoons to Liters (Three Steps)
- Start with 350 tablespoons.
- Convert tablespoons to cups: multiply by 1 cup/16 tablespoons.
- Convert cups to gallons: multiply by 1 gallon/16 cups.
- Convert gallons to liters: multiply by 3.785 liters/1 gallon.
- Calculation: 350 × 1/16 × 1/16 × 3.785/1 = 5.2 liters.
Key Terms & Definitions
- Conversion Factor — A ratio expressing how many of one unit are equal to another unit.
- Canceling Units — Arranging calculation so units divide out, leaving only the desired unit.
- Intermediate Unit — A unit used as a bridge in multi-step conversions.
Action Items / Next Steps
- Practice solving multi-step conversion problems, ensuring units cancel each time.
- Review unit relationships in relevant conversion tables or homework assignments.