Overview
This lecture covers metric prefixes, how to convert between different metric units using prefixes, and how to handle conversions involving squared and cubed units.
Metric Prefixes and Base Units
- Metric prefixes represent specific powers of ten attached to base units like grams, meters, or liters.
- A prefix example: mega- (M) means 10⁶, nano- (n) means 10⁻⁹.
- Any metric prefix can be combined with any base unit (e.g., kilograms (kg), milliliters (mL), megajoules (MJ)).
- Scientific notation makes expressing large or small numbers easier and clearer.
Converting Between Metric Prefixes
- Use dimensional analysis: write the given value and unit, multiply by a conversion factor with desired unit on top.
- To find the conversion factor, subtract exponents of the prefixes; the difference gives the power of ten needed.
- The larger unit gets "1", the smaller unit gets 10 to the exponent difference.
- Example: 2.6 kg to decigrams: exponent difference is 4, so 2.6 kg × 10⁴ dg/kg = 26,000 dg.
- Example: 18.2 nm to cm: exponent difference is -6, so 18.2 nm × 10⁻⁶ cm/nm = 1.82 × 10⁻⁶ cm.
Using Metric Prefixes with Other Units
- Prefixes are used with various units: milliliters (mL, 10⁻³ L), microseconds (μs), kilopascals (kPa), gigawatts (GW).
- Memorize common prefixes and their exponents for quick conversions.
Converting Squared and Cubed Units
- For squared (area) or cubed (volume) units, square or cube the linear conversion factor, respectively.
- Example: 1 km² = (10³ m)² = 10⁶ m².
- Example: 44.5 cm³ to dm³: exponent difference is 1 (linear), so cube it (1,000 cm³/dm³), giving 0.0445 dm³.
Key Terms & Definitions
- Prefix — A syllable added to base units to indicate a specific power of ten.
- Base unit — The fundamental metric unit (meter, gram, liter, etc.).
- Dimensional analysis — Technique for converting between units using conversion factors.
- Scientific notation — Expressing numbers as a coefficient times ten raised to an exponent.
Action Items / Next Steps
- Memorize metric prefixes and their associated exponents.
- Practice converting between units using dimensional analysis, including squared and cubed conversions.