Overview
This lecture explains traditional and chemistry-specific rounding rules for significant figures, detailing what to do when removing digits greater than, less than, or equal to five.
Traditional Rounding Rules
- If the digit being removed is greater than 5, increase the preceding digit by one.
- If the digit being removed is less than 5, keep the preceding digit the same.
- Example: Rounding 5.379 to three significant figures results in 5.38 (because 9 > 5, so 7 becomes 8).
- Example: Rounding 0.2413 to three significant figures results in 0.241 (because 3 < 5, so 1 stays 1).
Special Rounding Rule for Chemists (Rounding 5)
- If the digit removed is exactly 5, check if the preceding digit is odd or even.
- If the preceding digit is odd, increase it by one (make it even).
- If the preceding digit is even, keep it the same.
- Example: Rounding 17.75 to three significant figures gives 17.8 (7 is odd, becomes 8).
- Example: Rounding 17.65 to three significant figures gives 17.6 (6 is even, stays as 6).
Key Terms & Definitions
- Significant Figures (sigfigs) — the digits in a number that contribute to its precision.
- Traditional Rounding — increasing the preceding digit by one if the dropped digit is greater than 5; otherwise, it stays the same.
- Chemist's Rounding Rule for Five — if rounding off a 5, round up if the previous digit is odd, leave unchanged if even.
Action Items / Next Steps
- Practice rounding various numbers to a specified number of significant figures, especially focusing on cases where the digit being dropped is 5.