Overview
This lecture explains the rules for adding and subtracting numbers with significant figures, focusing on how to properly round answers based on decimal places.
Addition with Significant Figures
- First, perform the addition; round the result only after calculation.
- The final answer should have no more decimal places than the number in the problem with the fewest decimal places.
- To determine rounding, draw a vertical line just right of the digit with the fewest decimals; only keep digits to the left of the line.
- If adding more than two numbers, the rule for decimal places applies to all numbers in the sum.
Subtraction with Significant Figures
- Subtraction follows the same rule as addition regarding decimal places.
- Calculate first, then round the result to match the number with the fewest decimal places among those subtracted.
Layout of Numbers
- For horizontal problems, stack numbers vertically to clearly align decimal places before adding or subtracting.
- This helps to easily identify which digit determines the final number of decimal places.
Examples
- In 13.0198 + 1.2, the answer is rounded to one decimal place: 14.2.
- In 275.00 + 15 + 0.382, the answer is rounded to zero decimal places: 291.
- For 44.33 - 3.9922, the answer is rounded to two decimal places: 40.34.
- For 8.679 + 0.3 + 5.88, stack and sum, then round to one decimal place: 14.9.
Key Terms & Definitions
- Significant figures — Digits in a number that carry meaning for its precision.
- Decimal place — The position of a digit after the decimal point.
- Rounding — Adjusting a number to have the correct number of significant digits or decimal places.
Action Items / Next Steps
- Practice addition and subtraction problems using proper significant figure rules.
- Stack numbers vertically for clarity when aligning decimal places.
- Review class notes or textbook sections on significant figures for further examples.