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.