Overview
This lecture explains how to properly apply significant figures in mathematical calculations, focusing on addition, subtraction, multiplication, and division, along with correct rounding and notation.
Significant Figures in Calculations
- Significant figures (sig figs) limit a measurement to the correct number of digits.
- Apply sig fig rules after performing the calculation, not before.
- Rounding: If the last digit is ≥5, round up; if <5, round down.
Addition and Subtraction
- For addition/subtraction, limit the answer to the lowest number of decimal places in the original numbers.
- Example: 1.2 (1 decimal) + 4.71 (2 decimals) = 5.91 → rounded to 5.9 (1 decimal).
- Do not round individual numbers before adding/subtracting; round only the final result.
- Example: 101.2 (1 decimal) + 18.702 (3 decimals) = 119.902 → rounded to 119.9 (1 decimal).
- Subtraction example: 202.88 (2 decimals) – 1.013 (3 decimals) = 201.867 → rounded to 201.87 (2 decimals).
Multiplication and Division
- For multiplication/division, limit the answer to the fewest sig figs in any of the numbers used.
- Example: 23 (2 sig figs) ÷ 448 (3 sig figs) = 0.05133928 → rounded to 0.051 (2 sig figs).
- Example: 76.4 (3 sig figs) × 180.4 (4 sig figs) = 13782.56 → rounded to 13,800 (3 sig figs, no decimal).
- Example: 205,472.5275 (from division, 3 sig figs desired) → rounded to 205,000 (3 sig figs, placeholder zeros).
Scientific Notation and Zeros
- Scientific notation shows which zeros are significant by including only significant zeros in the coefficient.
- Example: 8.666 × 10⁶ has four sig figs.
- Writing numbers in scientific notation clarifies which zeros count as significant.
Key Terms & Definitions
- Significant Figures (Sig Figs) — Digits in a measurement that include all known digits plus one estimated digit.
- Placeholder Zero — A zero used to position the decimal point; not always significant unless specified.
- Decimal Places — The number of digits to the right of the decimal point.
- Scientific Notation — A way of writing numbers to clearly indicate significant figures.
Action Items / Next Steps
- Practice additional problems applying sig fig rules to calculations.
- Review which zeros are significant and how to use scientific notation for clarity.