Overview
This lecture explains scientific notation, unit prefixes, and dimensional analysis as tools for expressing and converting between very large or very small numbers in science.
Scientific Notation
- Scientific notation expresses numbers as a single digit, a decimal, and a power of ten (e.g., 5.3 × 10⁶).
- The exponent shows how many times to move the decimal point; positive for large, negative for small numbers.
- For example, 1.42 × 10² is 142, and 3.5 × 10⁻² is 0.035.
- Scientific notation simplifies writing and comparing very large or small quantities.
Unit Prefixes
- Unit prefixes represent specific powers of ten to indicate magnitude (e.g., kilo = 10³, nano = 10⁻⁹).
- Common prefixes: kilo (10³, thousand), nano (10⁻⁹, one billionth).
- Prefixes apply to any unit, such as meters, grams, or seconds, to express different scales.
Dimensional Analysis (Unit Conversion)
- Dimensional analysis uses fractions equal to one to convert between units without changing the value.
- To convert meters to nanometers, multiply by (10⁹ nm / 1 m); the meters cancel, leaving nanometers.
- For multi-step conversions (e.g., years to seconds), multiply by several fractions so all unwanted units cancel.
- Use known relationships (e.g., 365 days/year, 24 hours/day, 60 minutes/hour, 60 seconds/minute).
Key Terms & Definitions
- Scientific Notation — expressing numbers as a digit, decimal, and power of ten (e.g., 2.0 × 10⁵).
- Exponent — the number indicating how many times ten is used as a factor.
- Unit Prefix — a symbol before a unit that indicates a specific power of ten (e.g., kilo-, nano-).
- Dimensional Analysis — a method for converting units using fractions equal to one so units cancel appropriately.
Action Items / Next Steps
- Practice converting values between scientific notation and standard notation.
- Memorize common unit prefixes and their powers of ten.
- Complete exercises on dimensional analysis and unit conversions.