Overview
This lecture covers the rules for handling significant figures when adding and subtracting, highlighting their differences from multiplication/division and including examples and key notations.
Addition and Subtraction Sig Fig Rules
- For addition and subtraction, align decimal points and determine the least precise place value shared by all numbers.
- The final answer is rounded to this least precise (rightmost) place value.
- This method can increase or decrease the number of significant figures in your result.
Examples and Special Cases
- When adding 3.97 (rounded to the hundredths), the answer reflects the least shared decimal place (hundredths).
- Adding numbers like 3.24 and 7.23 can increase the number of significant digits in the sum.
- Subtracting numbers may drastically reduce the total significant figures (e.g., result of 0.1 from inputs with more sig figs).
Scientific Notation Considerations
- Before adding or subtracting, ensure all numbers are expressed with the same power of ten.
- Adjust the smaller exponent up to match the larger by shifting the decimal left.
- The addition may yield a result where a much smaller number does not change the significant digits of a much larger number.
Real-World Connection
- Measurement limitations depend on the tool (e.g., a ruler can't measure the width of a hair).
- Adding many measurements can expand results but cannot increase right-side precision beyond the least precise measurement.
Rounding and Propagation of Error
- Rounding after each calculation can propagate errors through multi-step problems.
- Carrying one extra, insignificant digit (using subscript notation) helps minimize error propagation in calculations.
- Subscripted digits indicate extra digits carried forward for precision, not for reporting.
Key Terms & Definitions
- Significant Figures (SigFigs) — The digits in a number that carry meaning for its precision.
- Place Value — The location of a digit in a number, determining its value (e.g., tenths, hundredths).
- Propagation of Error — The cumulative effect of rounding errors in sequential calculations.
- Scientific Notation — A way of expressing numbers as a product of a coefficient and a power of ten.
Action Items / Next Steps
- Write down and memorize the addition/subtraction sig fig rule.
- Practice problems involving significant figures in addition/subtraction and scientific notation.
- Be prepared to use subscript notation to carry insignificant digits in calculations.