Overview
This lecture explains the concept of significant figures (sig figs), rules for identifying them, and how to apply those rules in addition, subtraction, multiplication, and division, including with scientific notation.
Counting Significant Figures
- Nonzero digits are always significant.
- Zeros between nonzero digits are significant.
- Leading zeros (zeros to the left of a nonzero digit) are not significant.
- Trailing zeros without a decimal point are not significant.
- Trailing zeros with a decimal point are significant.
- In scientific notation, only digits in the base are significant.
Significant Figures in Calculations
Addition and Subtraction
- Align decimal points when adding or subtracting.
- Round the answer to the least number of decimal places present in any term.
- The position of the least certain digit (rightmost significant figure) determines the rounding.
Multiplication and Division
- Round the final answer to the least number of significant figures found in any term.
- Do not align decimal points; focus on the total count of sig figs.
Rounding Rules
- If the digit to be dropped is less than 5, round down; if 5 or greater, round up.
- When rounding, replace dropped places with zeros (for whole numbers) or stop at the correct decimal place.
Scientific Notation and Significant Figures
- When adding or subtracting, express numbers with the same exponent before combining.
- For multiplication, add exponents; for division, subtract exponents.
- Final answer must match the lowest number of sig figs among all numbers used.
Combined Operations
- Perform all calculations using exact intermediate values; only round the final answer.
- For mixed operations (e.g., add, then multiply), apply the correct sig fig rule at each step but only round at the end.
- Follow order of operations (PEMDAS) in all calculations.
Key Terms & Definitions
- Significant Figures (Sig Figs) — Digits that carry meaningful information about the precision of a number.
- Leading Zeros — Zeros before the first nonzero digit; not significant.
- Trailing Zeros — Zeros after the last nonzero digit; only significant with a decimal point.
- Scientific Notation — A method to express large or small numbers using powers of ten.
Action Items / Next Steps
- Practice identifying significant figures in various numbers.
- Complete practice problems on applying sig fig rules to addition, subtraction, multiplication, division, and scientific notation.
- Review order of operations for combined calculations.