How to Round Numbers to Significant Figures
Overview of Significant Figures
- Definition: Significant figures are the digits in a number that contribute to its precision.
- Identifying Significant Figures:
- The first significant figure is the first non-zero digit from left to right.
- Every digit after the first significant figure is also significant.
- Example:
- For 3,3476, the significant figures are 3 (first), 4 (second), 7 (third), 6 (fourth).
- For 0.004031, the significant figures are 4 (first), 0 (second), 3 (third), 1 (fourth).
- Zeros to the left of the first significant figure are not counted, but zeros to the right are significant.
Rounding to Significant Figures
Rounding Rules
- Last Digit: The digit at the place you are rounding to.
- Decider: The digit immediately after the last digit, which decides rounding direction.
- If the decider is 4 or less, keep the last digit the same.
- If the decider is 5 or more, round up the last digit.
Examples of Rounding
-
Rounding 3476 to Two Significant Figures:
- Last Digit: 4 (second significant figure).
- Decider: 7 (third digit).
- Since 7 is greater than 5, round 4 up to 5.
- Final rounded number: 3500.
-
Rounding 0.004031 to Three Significant Figures:
- Last Digit: 3 (third significant figure).
- Decider: 1 (fourth digit).
- Since 1 is 4 or less, keep 3 the same.
- Final rounded number: 0.00403.
Special Considerations
- Zeros at the End: When rounding decimal numbers, trailing zeros are not kept.
- Numbers Like 4300: Ambiguity exists whether it has two or four significant figures as it could have been rounded.
Key Takeaways
- Understanding which numbers are significant is crucial for precision.
- Decider determines whether the number is rounded up or stays the same.
- Rounding can introduce ambiguity in the count of significant figures, especially with trailing zeros.
This concludes the lecture on rounding numbers to significant figures. Understanding these principles is important for ensuring numerical accuracy in computations.