Overview
This lecture explains how to determine the correct number of significant figures (sigfigs) in answers to addition, subtraction, multiplication, and division problems, using clear rules and examples.
Addition and Subtraction Rules
- When adding or subtracting, match decimal places based on the least precise measurement.
- Visually line up numbers by decimal places before performing the operation.
- Draw a line after the last significant digit shared by all measurements to determine where to round.
- Enter all digits into your calculator, then round the answer to the position of the least precise value.
- Do not count total sigfigs; focus on decimal places.
- Zeros after a decimal point are significant; zeros without a decimal may not be.
- To minimize rounding error in multi-step problems, you can carry extra digits (not significant), but final answers must be rounded correctly.
Addition and Subtraction Examples
- Example: 103.65 + 48.3 = 151.95 → Round to 151.9 (tenths place, since 48.3's precision ends at tenths).
- Example: 54290.0 – 68147.0 = -13857.0 → Round according to last significant decimal place.
- Example: 2,451,000 – 800,000 = 1,651,000 → Round to 1,700,000 when sigfigs allow only two digits.
Scientific Notation & Sigfigs
- Scientific notation preserves the number of sigfigs that standard notation may not.
- Use scientific notation especially when a precise number of sigfigs is needed but standard form is ambiguous.
Multiplication and Division Rules
- For multiplication and division, the answer must have the same number of sigfigs as the measurement with the fewest sigfigs.
- Count sigfigs in each value before calculating.
- Calculators do not enforce sigfig rules; adjust the answer as needed based on sigfigs.
Multiplication and Division Examples
- 2.70 ÷ 1.00 = 2.70 (3 sigfigs; calculator may show 2.7, so add a zero).
- 2 × 7 = 10 (1 sigfig, despite calculator saying 14).
- 2.0 × 7.0 = 14 (2 sigfigs, do not write 14.0).
- Adjust zeros as necessary to reflect required sigfigs.
Key Terms & Definitions
- Significant Figures (Sigfigs) — Digits in a number that carry meaning regarding its precision.
- Precision — The smallest place value in a measurement that is reliable.
- Scientific Notation — A way to express numbers to preserve correct sigfigs.
- Rounding — Adjusting numbers to reflect correct precision or sigfigs.
Action Items / Next Steps
- Practice identifying significant figures and determining the correct rounding for various types of problems.
- Review any homework or problems involving sigfigs, especially using both addition/subtraction and multiplication/division rules.