Dimensional Analysis and Unit Conversions

Jun 8, 2024

Dimensional Analysis and Unit Conversions Lecture

Key Concepts

  • Dimensional Analysis: A systematic method to convert units by multiplying by conversion factors arranged to cancel out unwanted units.
  • Unit Conversions: Switching a quantity expressed in one set of units to another set of units using conversion factors.

Examples Discussed

English to English Conversion

Problem: Convert 0.0067 miles to inches.

**Provided Information: **

  • 12 inches = 1 foot.
  • 5280 feet = 1 mile.

**Steps: **

  1. Start with 0.0067 miles.
  2. Convert miles to feet:
    • Place 1 mile in the denominator and 5280 feet in the numerator to cancel out miles.
    • Calculate the feet.
  3. Convert feet to inches:
    • Place 1 foot in the denominator and 12 inches in the numerator to cancel out feet.
  4. Calculate the inches.
    • Result: 424.5 inches, which is rounded to 420 inches or 4.2 x 10² inches for significant figures.

Metric to Metric Conversion

Problem: Convert 0.45 kilograms to milligrams.

**Steps: **

  1. Start with 0.45 kilograms.
  2. Convert kilograms to grams:
    • 1 kilogram = 1000 grams.
  3. Convert grams to milligrams:
    • 1 gram = 1000 milligrams.
  4. Calculate the milligrams.
    • Result: 450,000 milligrams, which is 4.5 x 10⁵ milligrams for significant figures.

Mixed English to Metric Conversion

Problem: Convert 0.0488 gallons to centiliters.

**Provided Information: **

  • 4 quarts = 1 gallon.
  • 1 quart = 946 milliliters.
  • 100 centiliters = 1 liter.

**Steps: **

  1. Start with 0.0488 gallons.
  2. Convert gallons to quarts:
    • 1 gallon = 4 quarts.
  3. Convert quarts to milliliters:
    • 1 quart = 946 milliliters.
  4. Convert milliliters to centiliters:
    • 100 milliliters = 1 deciliter.
  5. Calculate the centiliters.
    • Result: 18 centiliters.

Density Conversion

Problem: Convert 6.23 ounces per cup to decigrams per milliliter.

**Provided Information: **

  • 16 ounces = 1 pound.
  • 2.2 pounds = 1 kilogram.
  • 1 quart = 946 milliliters.
  • 4 cups = 1 quart.
  • 10 decigrams = 1 gram

**Steps: **

  1. Set up the initial density: 6.23 oz/cup.
  2. Convert ounces to pounds:
    • 16 ounces = 1 pound.
  3. Convert pounds to kilograms:
    • 2.2 pounds = 1 kilogram.
  4. Convert kilograms to grams:
    • 1 kilogram = 1000 grams.
  5. Convert grams to decigrams:
    • 1 gram = 10 decigrams.
  6. Calculate the results for the mass portion.
  7. Convert cups to milliliters via quarts:
    • 4 cups = 1 quart
    • 1 quart = 946 milliliters
  8. Calculate the final density.
    • Result: 7.48 decigrams per milliliter.