Overview
This lecture covers unit conversions between the imperial and metric (SI) systems, outlining step-by-step methods and addressing significant figures in the calculations.
Basics of Unit Conversion
- Always start problems with the quantity and unit given.
- Set up conversions to cancel out unwanted units step by step.
- Use provided relationships (e.g., 1 inch = 2.54 cm) to convert between units.
Example 1: Inches to Kilometers
- Start with 494 inches.
- Convert inches to centimeters using 1 inch = 2.54 cm.
- Convert centimeters to meters (1 cm = 10^-2 m).
- Convert meters to kilometers (1 km = 10^3 m).
- Multiply/divide accordingly: 494 × 2.54 × 10^-2 ÷ 10^3.
- Round final answer to three significant figures due to the measurement's precision.
Example 2: Picoliters to Gallons
- Start with 3.594 × 10^7 picoliters.
- Convert picoliters to liters (1 pL = 10^-12 L).
- Convert liters to milliliters (1 L = 10^3 mL).
- Convert milliliters to quarts (1 qt = 946.353 mL).
- Convert quarts to pints (1 qt = 2 pints).
- Convert pints to gallons (1 gallon = 8 pints).
- Use only the measured values' significant figures for the final answer (here: four sig figs).
Significant Figures in Conversions
- Count the significant figures in measured values; defined relationships (like 1 inch = 2.54 cm) are exact.
- The answer should have the same number of significant figures as the least precise measured value in the calculation.
Calculator Tips for Scientific Notation
- Enter numbers using the 'E' key: e.g., 3.594E7 means 3.594 × 10^7.
- Use '1E' for the power of ten, not '10E'.
- When dividing by multiple numbers, enter each bottom value separately as a division.
Example 3: Miles to Millimeters
- Start with 239,000 miles.
- Convert miles to kilometers using a given relationship.
- Convert kilometers to meters (1 km = 10^3 m).
- Convert meters to millimeters (1 m = 10^3 mm).
- The final answer's significant figures are based on the least precise measured value.
Key Terms & Definitions
- Imperial System — A non-metric system of measurement (inches, feet, miles, etc.).
- SI System (International System of Units) — The modern metric system (meters, liters, grams, etc.).
- Significant Figures (sig figs) — Digits that carry meaningful information about measurement precision.
- Exact Value — A value defined by definition, not by measurement (e.g., conversion factors).
Action Items / Next Steps
- Practice similar unit conversion problems in your homework.
- Review calculator instructions for entering scientific notation correctly.
- Write down "Beast Boy" and "Storm Troopers" as directed.