To determine which of the given numbers is expressed with the correct number of significant figures, we first need to understand the rules for identifying significant figures. ### Significant Figures Rules: 1. **Non-zero digits** are always significant. For example, in the number 123, all three digits (1, 2, and 3) are significant. 2. **Any zeros between significant digits** are also significant. For example, in 105, the zero is significant because it is between the 1 and the 5. 3. **Leading zeros** (zeros to the left of the first non-zero digit) are not significant. For example, in 0.00456, the leading zeros are not counted as significant figures. 4. **Trailing zeros** in a number with a decimal point are significant. For example, in 123.4500, the zeros after the 5 are significant because they indicate precision. 5. **Trailing zeros** in a whole number without a decimal point are ambiguous and may or may not be significant. For example, in 1000, it is unclear how many significant figures are intended unless specified. ### Analyzing Each Option: Now, let's analyze each option based on these rules: **A. 0.00456** - The leading zeros (0.00) are not significant. - The significant figures are 4, 5, and 6. - **Total significant figures: 3.** **B. 123.4500** - All digits (1, 2, 3, 4, 5, and the two trailing zeros) are significant. - **Total significant figures: 6.** **C. 0.0007890** - The leading zeros (0.000) are not significant. - The significant figures are 7, 8, 9, and the trailing zero (0) after 9 is significant because it indicates precision. - **Total significant figures: 4.** **D. 1000** - The number of significant figures is ambiguous because there is no decimal point. - It could be interpreted as having 1 significant figure (1) or 4 significant figures (1000) depending on the context. - **Total significant figures: Ambiguous.** ### Conclusion: Based on the analysis, the option with the correct number of significant figures is **B. 123.4500**, which has 6 significant figures. ### Why Other Options Are Incorrect: - **A. 0.00456**: While it has 3 significant figures, it is not the highest count among the options. - **C. 0.0007890**: This has 4 significant figures, which is also not the highest count. - **D. 1000**: The ambiguity in significant figures makes it less precise compared to the other options. ### Revision Summary: - Significant figures are determined by specific rules regarding non-zero digits, leading zeros, and trailing zeros. - Option B (123.4500) has the highest and clear count of significant figures (6). - Leading zeros do not count as significant figures, while trailing zeros after a decimal do. - Whole numbers without a decimal point can be ambiguous in their significant figure count.