Overview
This lecture explains how to correctly use significant figures in calculations, focusing on addition, subtraction, multiplication, division, and operations with powers and roots.
Addition and Subtraction with Significant Figures
- Round your answer to the same decimal place as the value with its rightmost significant figure in the greatest decimal place.
- Example: 4.03 + 5.4 → round to tenths (answer: 9.4).
- If a number lacks a decimal, trailing zeros may not be significant; round based on the leftmost uncertain digit.
- Example: 510 - 418, round to tens (answer: 90).
- With decimals, all zeros after the decimal are significant; round accordingly.
- Example: 4300. - 4182. → round to ones (answer: 4418).
- For scientific notation, identify decimal places before rounding.
- Always match the answer's decimal place to the least precise value used.
Multiplication and Division with Significant Figures
- Round your answer to the same number of significant figures as the value with the fewest sig figs.
- Ignore decimal place position; only count the total number of significant digits.
- Example: 3 sig figs × 1 sig fig → answer with 1 sig fig.
- Example: 4 sig figs ÷ 2 sig figs → answer with 2 sig figs.
- Zeros may or may not be significant; a decimal point can make trailing zeros significant.
- Adjust decimal points or convert to scientific notation as needed to match the correct number of significant figures.
Powers and Roots with Significant Figures
- Round your answer to the same number of significant figures as the original number being raised or rooted.
- Example: (number with 3 sig figs)^4 → answer with 3 sig figs.
- Example: sqrt(number with 2 sig figs) → answer with 2 sig figs (e.g. 4.0).
- Write answers in scientific notation when it helps preserve significant figures (e.g., 2.1 × 10^2).
Key Terms & Definitions
- Significant Figures (sig figs) — digits in a number that carry meaning for its precision.
- Decimal Place — the position of a digit to the right of the decimal point.
- Scientific Notation — a way to represent numbers using powers of ten.
- Root — the inverse operation of raising to a power (e.g., square root, cube root).
Action Items / Next Steps
- Practice sample problems using each rule for addition, subtraction, multiplication, division, and roots/powers with significant figures.
- Review scientific notation to ensure correct application of significant figure rules.