Overview
This lecture focuses on metric unit prefixes, their meanings, and systematic methods for converting between units using these prefixes, with practical tips for accurate conversions and reporting.
Metric vs. English Unit Systems
- English units (inches, feet, yards, miles) use irregular conversion factors, making calculations cumbersome.
- The metric system uses prefixes based on powers of 10, making conversions straightforward.
Common Metric Prefixes and Meanings
- Metric prefixes modify unit size by powers of 10 and can be applied to any unit (meter, gram, liter, etc.).
- Larger units: tera- (10¹²), giga- (10⁹), mega- (10⁶), kilo- (10³).
- Smaller units: deci- (10⁻¹), centi- (10⁻²), milli- (10⁻³), micro- (10⁻⁶), nano- (10⁻⁹), pico- (10⁻¹²).
- Mnemonics (e.g., "the great mighty king died choking on mini metal nails") can help memorize prefixes.
Principles for Using Unit Prefixes
- Use prefixes to keep reported numbers between 1 and 1,000 for clarity and usefulness.
- Prefixes act as conversion factors and can apply to any measurable quantity.
Conversion Techniques
- To convert units, always set up with the unit you want to cancel opposite your starting value.
- Place a "1" in front of the larger unit and the appropriate power of 10 (positive exponent) in front of the smaller unit.
- When the prefix exponent does not match, shift the decimal and adjust the exponent accordingly until it matches a standard prefix.
- Always maintain the same number of significant figures during conversions.
Example Conversions
- 400 microliters to liters: 400 μL × (1 L / 10⁶ μL) = 4 × 10⁻⁴ L.
- 3.757 millimeters to meters: 3.757 mm × (1 m / 10³ mm) = 3.757 × 10⁻³ m.
- 1.99 megayears to years: 1.99 My × (10⁶ y / 1 My) = 1.99 × 10⁶ y.
Best Practices in Calculations and Reporting
- Use scientific notation for very large or small numbers to ease conversion to prefixes.
- Watch for correct upper/lowercase usage (e.g., M = mega, m = milli).
- Be aware that conventions like "mcg" may be used for micrograms in health contexts, though this is technically incorrect.
Using Calculators Effectively
- Enter scientific notation properly (use "E" or "EXP" keys).
- Check for appropriate significant figures in calculator outputs, especially with TI calculators.
Key Terms & Definitions
- Metric Prefix — A word part attached to a unit indicating multiplication by a power of ten.
- Scientific Notation — Way of expressing numbers as a product of a coefficient and a power of ten.
- Significant Figures (Sig Figs) — Number of meaningful digits in a measurement.
- Conversion Factor — A ratio expressing how many of one unit equals another.
Action Items / Next Steps
- Memorize the key metric prefixes and their powers of ten.
- Practice single- and two-step metric conversions using provided online resources.
- Review calculator functions for inputting scientific notation and displaying significant figures.
- Ensure all reported measurements use an appropriate prefix to keep numeric values between 1 and 1,000.