Overview
The lecture covers significant figures (sig figs) and scientific notation, focusing on their definitions, rules for counting significant digits, and how to use them in calculations.
Exact vs. Inexact Numbers
- Exact numbers result from counting or definitions (e.g., 10 fingers, 100 cm in 1 m).
- Inexact numbers arise from measurements, which include uncertainty in the last digit.
Significant Figures Rules
- Significant figures include all certain digits plus one estimated digit in a measured value.
- Nonzero digits are always significant.
- Zeros between nonzero digits ("sandwiches") are significant.
- Zeros after a nonzero digit and after a decimal point are significant.
- Zeros at the start of a number or at the end without a decimal are not significant (placeholders).
Counting Significant Figures in Zeros
- Sandwich zeros (e.g., 1002) are significant.
- Trailing zeros with a decimal (e.g., 2.300) are significant.
- Leading zeros (e.g., 0.0023) are not significant.
- Trailing zeros without a decimal (e.g., 2500) are not significant unless a decimal is shown (2500.0).
- A decimal at the end (e.g., 2570.) makes the trailing zero significant.
Rounding and Calculations
- For multiplication/division, the result should match the measurement with the fewest significant figures.
- For addition/subtraction, the answer should match the least precise decimal place among the numbers used.
- Round up if the dropped digit is 5 or more; round down if 4 or less.
Scientific Notation
- Written as a coefficient (1 to <10) times 10 to a whole-number exponent.
- Positive exponent: number is greater than one.
- Negative exponent: number is less than one.
- The exponent equals the number of places moved to get the coefficient between 1 and 10.
- Use positive exponents for big numbers, negative for small numbers.
Key Terms & Definitions
- Significant Figures (sig figs or SF) — all certain digits and the first uncertain digit in a measurement.
- Exact Number — number known with complete certainty, from counting or definitions.
- Inexact Number — measured value with uncertainty in its last digit.
- Sandwich Zero — zero between nonzero digits, always significant.
- Scientific Notation — a method of expressing numbers as a coefficient times 10 to some exponent.
Action Items / Next Steps
- Review place value terminology (ones, tenths, hundredths, etc.).
- Practice determining significant figures in various numbers.
- Practice converting numbers to and from scientific notation.
- Prepare for in-class practice on these topics next session.