To determine which of the given numbers is correctly rounded to three significant figures, we first need to understand what significant figures are and how to round numbers accordingly. ### Understanding Significant Figures **Significant figures** are the digits in a number that contribute to its precision. This includes: - All non-zero digits (1-9). - Any zeros between significant digits. - Leading zeros (zeros before the first non-zero digit) are **not** significant. - Trailing zeros in a decimal number are significant. ### Analyzing Each Option Now, let's analyze each option to see which one is correctly rounded to three significant figures. #### Option A: 0.004567 - **Significant Figures**: The leading zeros do not count, so we start counting from the first non-zero digit, which is 4. The significant figures are 4, 5, and 6. - **Rounded to Three Significant Figures**: The number rounded to three significant figures is 0.00457 (the last digit is rounded up from 6 to 7). - **Conclusion**: This option is **not** correctly rounded to three significant figures as it is presented as 0.004567. #### Option B: 123.456 - **Significant Figures**: All digits are significant here (1, 2, 3, 4, 5, and 6). - **Rounded to Three Significant Figures**: The first three significant figures are 1, 2, and 3. The number rounded to three significant figures is 123 (the next digit, 4, does not affect rounding). - **Conclusion**: This option is correctly rounded to three significant figures. #### Option C: 7.8901 - **Significant Figures**: All digits are significant (7, 8, 9, 0, and 1). - **Rounded to Three Significant Figures**: The first three significant figures are 7, 8, and 9. The number rounded to three significant figures is 7.89 (the next digit, 0, does not affect rounding). - **Conclusion**: This option is **not** correctly rounded to three significant figures as it is presented as 7.8901. #### Option D: 0.0001234 - **Significant Figures**: The leading zeros do not count, so we start counting from the first non-zero digit, which is 1. The significant figures are 1, 2, and 3. - **Rounded to Three Significant Figures**: The number rounded to three significant figures is 0.000123 (the next digit, 4, does not affect rounding). - **Conclusion**: This option is **not** correctly rounded to three significant figures as it is presented as 0.0001234. ### Summary of Options - **A**: 0.004567 → Not correctly rounded (should be 0.00457). - **B**: 123.456 → Correctly rounded (is 123). - **C**: 7.8901 → Not correctly rounded (should be 7.89). - **D**: 0.0001234 → Not correctly rounded (should be 0.000123). ### Final Answer The correct option is **B**. ### Revision Summary - Significant figures include all non-zero digits and zeros between them, but not leading zeros. - Rounding to three significant figures involves identifying the first three significant digits and rounding based on the next digit. - Option B (123.456) is the only number correctly rounded to three significant figures as 123. - Always check the context of the number (leading/trailing zeros) when determining significant figures.