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Unit Conversion Using Dimensional Analysis

Aug 30, 2025

Overview

This lecture demonstrates how to use dimensional analysis to convert 365.0 picometers to feet using provided conversion factors.

Step-by-Step Conversion Process

  • Start with the value to convert: 365.0 picometers (pm).
  • Remember or look up that 1 meter (m) = 1 × 10¹² picometers.
  • Convert picometers to meters by dividing by 1 × 10¹².
  • Result after first step: 3.65 × 10⁻¹⁰ meters.
  • Use the given conversion: 1 meter = 39.4 inches (in).
  • Convert meters to inches by multiplying by 39.4.
  • Result after second step: 1.438 × 10⁻⁸ inches.
  • Use the given conversion: 12 inches = 1 foot (ft).
  • Convert inches to feet by dividing by 12.
  • Final result: 1.198 × 10⁻⁹ feet (rounded to 4 significant figures).

Converting Units: Key Steps

  • Set up conversion factors so units cancel out step by step.
  • Multiply by the top of the fraction, divide by anything on the bottom.
  • Carefully track and cancel units at each step to avoid mistakes.

Significant Figures

  • The original number (365.0) has 4 significant figures.
  • The final answer should also be reported with 4 significant figures: 1.198 × 10⁻⁹ ft.

Key Terms & Definitions

  • Dimensional Analysis — A method for converting between units using conversion factors.
  • Picometer (pm) — A metric unit of length equal to 1 × 10⁻¹² meters.
  • Significant Figures — The digits in a measurement that are meaningful in terms of accuracy.

Action Items / Next Steps

  • Practice similar unit conversion problems using dimensional analysis.
  • Review and memorize common metric conversion factors for future problems.