Overview
This lecture covers significant figures in calculations (rounding, multiplication, division) and introduces metric system prefixes and equality statements for unit conversions.
Significant Figures and Rounding
- Significant figures (sig figs) indicate the precision of a measured value.
- Rounding rules: If the digit after the last sig fig is 5 or more, round up; if 4 or less, leave unchanged.
- Leading zeros are not significant; trailing zeros after a decimal are significant.
- Example: 1.854 kg rounded to two sig figs is 1.9 kg; 0.004738265 cm rounded is 0.0047 cm or 4.7 × 10⁻³ cm.
Significant Figures in Calculations
- For multiplication/division, the result should have the same number of sig figs as the input with the fewest sig figs.
- Example: 400 × 185 = 74,000 but rounds to 70,000 (1 sig fig).
- Example: 0.825 × 3.6 × 5.1 = 15.147 but rounds to 15 (2 sig figs).
- When using scientific notation, multiply/divide the digit terms and add/subtract the exponents.
Using Scientific Notation in Calculations
- Multiply digit terms and add exponents; divide digit terms and subtract exponents.
- Always report the answer in proper scientific notation (single digit before the decimal).
- Example: 0.637 × 10⁷ = 6 × 10⁶ after adjusting notation and sig figs.
- Carry one extra digit during multi-step calculations to avoid rounding errors.
Metric System Prefixes and Equalities
- Metric prefixes (kilo, mega, milli, micro, pico, etc.) simplify reporting large/small numbers.
- Example: 1 gigameter (Gm) = 10⁹ meters; 1 millimeter (mm) = 10⁻³ meters.
- Prefixes can be applied to any SI base unit (meter, gram, liter, second).
- Equality statements: 1 megagram (Mg) = 10⁶ grams; 1 gram = 0.001 kilograms.
Metric Conversions and Relationships
- 1 megagram = 1,000,000 grams.
- 1 milliliter = 1,000 microliters.
- 1 gram = 0.001 kilograms.
- 1 gram = 1,000 milligrams.
- Use cancellation of units and exponents to convert between prefixes.
Key Terms & Definitions
- Significant Figures (Sig Figs) — Digits in a number that reflect measurement precision.
- Scientific Notation — Number format as a digit term × 10 to a power.
- Metric Prefix — A symbol representing a fixed multiple or fraction of a base unit (e.g., kilo = 10³).
- Equality Statement — Shows equivalence between units (e.g., 1 km = 1,000 m).
Action Items / Next Steps
- Memorize common metric prefixes (kilo, mega, milli, micro, nano, pico).
- Practice identifying significant figures and rounding numbers.
- Work example problems converting between metric units using prefixes.