Overview
This lecture covers measurement in science, focusing on uncertainty, scientific notation, significant figures, and the proper use of units in calculations.
Uncertainty in Measurement
- Scientific values report only digits known with certainty; the last digit is the first uncertain digit.
- Uncertainty is shown as ± the value of the last digit (e.g., 0.6°C ± 0.1°C).
- This reflects the possible range, making results meaningful and reliable for decision-making.
Scientific Notation
- Scientific notation expresses numbers as a decimal (1–10) times a power of 10.
- Positive exponents indicate large numbers (e.g., 10³ = 1,000).
- Negative exponents indicate small numbers (e.g., 10⁻³ = 0.001).
- Move the decimal to create a number between 1 and 10; the number of moves is the exponent.
Reading Scales & Estimating
- Always record digits you are sure of from the scale; the first uncertain digit is estimated.
- The position and divisions on the scale determine how many digits you report.
- Report the value to the smallest marked interval, then estimate one more digit.
Significant Figures (Sig Figs)
- Non-zero digits are always significant.
- Trapped zeros (between non-zero digits) are significant.
- Trailing zeros are significant if there’s a decimal point shown.
- Preceding zeros (before the first non-zero digit) are not significant.
- Exact numbers (counted values, constants, and defined conversions) have infinite significant figures.
Counting and Rounding Sig Figs
- When rounding, look only at the first digit to be removed: round up if it’s 5 or greater.
- Only round at the end of calculations to avoid error propagation.
- For rounding, keep only as many significant figures as needed.
Sig Figs in Calculations
- For multiplication/division, keep the fewest sig figs among the values used.
- For addition/subtraction, keep the fewest decimal places among the values.
- Do not count the exponent in scientific notation when determining significant figures.
Key Terms & Definitions
- Uncertainty — The range within which the true value lies, shown as ± the last digit.
- Scientific Notation — A way to express numbers as a decimal between 1–10 times a power of 10.
- Significant Figures — Digits in a number that represent known values, plus one estimated digit.
- Exact Numbers — Values known without uncertainty (counted quantities, definitions, constants).
Action Items / Next Steps
- Practice identifying and counting sig figs in various numbers.
- Complete rounding and calculation exercises using sig fig rules.
- Review homework involving unit conversions and scientific notation.