Overview
This lecture covers how to use conversion factors for unit conversions (especially chained conversions), significant figures in calculations, and temperature scales/conversions.
Conversion Factors and Unit Conversions
- Conversion factors are equalities between two units that can be written as fractions to cancel unwanted units.
- To convert units (e.g., pints to liters), chain conversion factors into one long calculation instead of solving each step separately.
- Place the unit you want to cancel in the denominator of the next fraction, and continue until you reach the desired unit.
- On exams, conversion factors will be given as equalities, not as fractions; you must set up the correct fraction yourself.
- Multiply numerators and divide denominators step by step as you go through each conversion factor.
- There's a practice website to help with arranging conversion factors, which will be posted on D2L.
Significant Figures in Calculations
- When multiplying/dividing, the answer should have the same number of significant figures as the value with the fewest sig figs.
- Exact conversion factors within the same system (e.g., pints to quarts) do not affect sig figs; between systems, most are measured except 2.54 cm = 1 in (exact).
- Usually, the number of sig figs you start with is the number you end with, but check the rules for each type of calculation.
- Significant figures are more important in lab work than on lecture exams.
Temperature and Temperature Scales
- Temperature measures how hot or cold something is, reflecting particle motion.
- Three temperature scales: Fahrenheit (°F), Celsius (°C), and Kelvin (K); Kelvin has no degree symbol.
- Formulas for converting between scales are provided on the formula sheet given during tests and quizzes.
- Treat constants in temperature formulas as exact (infinite sig figs) for calculations.
- Remember: Addition/subtraction rules use decimal places, not sig figs; multiplication/division uses sig figs.
- Practice rearranging temperature conversion formulas, as you may not be given every form.
Key Terms & Definitions
- Conversion Factor — An equality between two units, written as a fraction to convert between them.
- Significant Figures — Digits in a measurement that include all known digits plus one estimated digit, reflecting precision.
- Exact Number — A value known with complete certainty, often from definitions or counting.
- Celsius (°C) — Temperature scale based on water’s freezing (0°C) and boiling (100°C) points.
- Fahrenheit (°F) — Temperature scale commonly used in the US, not based on water properties.
- Kelvin (K) — Absolute temperature scale, starts at absolute zero, no negative values.
Action Items / Next Steps
- Review section 1.7 for more on conversion factors.
- Practice setting up chained conversions using the provided website and textbook tables.
- Refer to the formula sheet for temperature conversions and practice rearranging formulas.
- Complete assigned homework problems for extra practice.
- Ask for help during class or office hours if you’re struggling with these processes.