The Metric System

Metric Prefixes

  • Mega (10610^6): Million

  • Kilo (10310^3): Thousand

  • Hecto (10210^2): Hundred

  • Deca (10110^1): Ten

  • Deci (10−110^{-1}): Tenth

  • Centi (10−210^{-2}): Hundredth

  • Milli (10−310^{-3}): Thousandth

  • Micro (10−610^{-6}): Millionth

Conversion Methods

  1. Metric Stairs (Decimal Shift)

    • A mental model where each step represents a decimal place shift.

    • Moving Down (smaller units): Move the decimal to the right.

      • Example: 5.5 cm=55 mm5.5 \text{ cm} = 55 \text{ mm}.

    • Moving Up (larger units): Move the decimal to the left.

      • Example: 93.2 m=0.000932 Mm93.2 \text{ m} = 0.000932 \text{ Mm}.

  2. Dimensional Analysis

    • A methodical approach using conversion factors and equivalence statements.

    • Single-step: 12.112 m×1000 mm1 m=12,112 mm12.112 \text{ m} \times \frac{1000 \text{ mm}}{1 \text{ m}} = 12,112 \text{ mm}.

    • Two-step: Convert to a base unit first, then to the target unit.

      • Example: 4.6 hl×100 L1 hl×1000 ml1 L=460,000 ml4.6 \text{ hl} \times \frac{100 \text{ L}}{1 \text{ hl}} \times \frac{1000 \text{ ml}}{1 \text{ L}} = 460,000 \text{ ml}.