si units & prefixes:

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Used to express quantities that span from extremely large (e.g., distances in space) to extremely small (e.g., atomic scales)

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Derived Units:

• Speed: meters per second (m/s)
• Force: newton (N) = kg·m/s²
• Pressure: pascal (Pa) = N/m

scalars vs vectors:

• Vectors have magnitude and direction. Scalars have magnitude only.

scientific notation & orders of magnitude:

• Scientific Notation: Used for very large/small numbers.

  • Example:
    • 5,000,000 = 5 × 10⁶
    • 0.000003 = 3 × 10⁻⁶

• Order of Magnitude:

  • Based on powers of 10; used to compare the scale of values.
  • Rule:
    • If power of 10 ≥ 5 → increase magnitude by 1
    • If < 5 → magnitude stays the same
  • Example:
    • 1 km = 10³ m
    • 1 mm = 10⁻³ m

Range of Magnitudes in the Universe:

• Distances:
  • Atom ≈ 10⁻¹⁰ m
  • Earth to Sun ≈ 10¹¹ m
• Masses:
  • Electron ≈ 10⁻³¹ kg
  • Sun ≈ 10³⁰ kg
• Time:
  • Nuclear reaction ≈ 10⁻²³ s
  • Age of the universe ≈ 10¹⁷ s

significant figures & rounding rules:

• Used to express the certainty in a measurement.