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Metric Prefixes and Conversion

Aug 30, 2025

Overview

This lecture explains metric prefixes, how to interpret their meaning, and how to convert between units using exponent subtraction.

Metric Prefixes and Base Units

  • Metric prefixes are shorthand symbols representing powers of ten used with base units like gram, meter, or liter.
  • Each prefix has a symbol and represents a specific exponent of ten (e.g., kilo = 10³, centi = 10⁻²).
  • The base unit (no prefix) always represents 1 or 10⁰.
  • Examples: 1 kilogram (kg) = 10³ grams; 1 centimeter (cm) = 10⁻² meters; 8 milliliters (mL) = 8 × 10⁻³ liters.

Converting Between Metric Prefixes

  • Use a chart listing prefixes, their symbols, and exponents to facilitate conversions.
  • Conversion Steps:
    • Subtract the starting prefix exponent from the target prefix exponent.
    • Move the decimal in the original number by the result's value (right for positive, left for negative).
    • Fill in any blank decimal places with zeros.

Conversion Examples

  • 0.150 meters (base unit, exponent 0) to centimeters (centi, exponent -2): 0 - (-2) = 2; move decimal 2 right → 15.0 cm.
  • 0.150 kilometers (kilo, 3) to centimeters (centi, -2): 3 - (-2) = 5; move decimal 5 right → 15,000 cm.
  • 384.0 milligrams (milli, -3) to decigrams (deci, -1): (-1) - (-3) = 2; move decimal 2 left → 3.84 dg.
  • 1 liter (base, 0) to megaliters (mega, 6): 0 - 6 = -6; move decimal 6 left → 0.000001 ML.

Key Terms & Definitions

  • Metric Prefix — a symbol and value showing a power of ten for a base unit.
  • Base Unit — a fundamental unit (meter, liter, gram) with exponent 0.
  • Exponent — the power of ten that defines the metric prefix's value.

Action Items / Next Steps

  • Review the metric prefix chart linked in the description.
  • Practice converting between units using exponent subtraction and decimal movement.
  • Attempt problem #4 from the lecture as self-practice.