To determine which of the given options is expressed to the correct number of significant figures based on the measurement of 0.004560 meters, we first need to understand the concept of significant figures. ### Step-by-Step Explanation 1. **Understanding Significant Figures**: - Significant figures (or significant digits) are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and trailing zeros in the decimal portion. - In the number 0.004560, the significant figures are counted as follows: - The leading zeros (0.00) are not significant; they only indicate the position of the decimal point. - The digits 4, 5, and 6 are significant. - The trailing zero (0) after the 6 is significant because it indicates the precision of the measurement. 2. **Counting Significant Figures in 0.004560**: - The number 0.004560 has **five significant figures**: 4, 5, 6, and the trailing 0. 3. **Analyzing the Options**: - **Option A: 0.00456** - This number has four significant figures (4, 5, and 6). The trailing zero is missing, which means it does not convey the same level of precision as the original measurement. **Incorrect.** - **Option B: 0.004560** - This number has five significant figures (4, 5, 6, and the trailing 0). It accurately reflects the precision of the original measurement of 0.004560 meters. **Correct.** - **Option C: 0.0045600** - This number has six significant figures (4, 5, 6, and two trailing zeros). While it is more precise than the original measurement, it implies a level of precision that is not supported by the original measurement. **Incorrect.** - **Option D: 0.005** - This number has only three significant figures (5 and the leading zeros are not counted). It does not reflect the precision of the original measurement. **Incorrect.** ### Conclusion The correct option is **B: 0.004560** because it accurately represents the five significant figures of the original measurement of 0.004560 meters. ### Summary of Why Other Options Are Incorrect - **Option A**: Lacks the trailing zero, thus only has four significant figures. - **Option C**: Has an extra trailing zero, indicating more precision than the original measurement. - **Option D**: Significantly reduces the number of significant figures to three, losing important precision. ### Revision Summary - Significant figures include all non-zero digits, zeros between them, and trailing zeros in decimal numbers. - The number 0.004560 has five significant figures. - The correct representation of this measurement is 0.004560 (Option B). - Be cautious of leading and trailing zeros when determining significant figures.