To determine which of the given numbers is rounded to three significant figures, we first need to understand what significant figures are. Significant figures are the digits in a number that contribute to its precision. This includes all non-zero digits, any zeros between significant digits, and any trailing zeros in the decimal portion. ### Step-by-Step Explanation 1. **Identify Significant Figures**: - **0.00456789**: The significant figures start from the first non-zero digit. Here, the significant figures are 4, 5, 6, 7, 8, and 9. Thus, this number has 6 significant figures. - **123.456**: All digits are non-zero, so this number has 6 significant figures (1, 2, 3, 4, 5, and 6). - **0.00098765**: The significant figures start from the first non-zero digit, which is 9. The significant figures are 9, 8, 7, 6, and 5. This number has 5 significant figures. - **4567.89**: All digits are non-zero, so this number has 6 significant figures (4, 5, 6, 7, 8, and 9). 2. **Rounding to Three Significant Figures**: - To round a number to three significant figures, we look at the first three significant digits and then consider the next digit to determine whether to round up or keep it the same. - **0.00456789**: The first three significant figures are 4, 5, and 6. The next digit is 7, which means we round up. Thus, it becomes **0.00457**. - **123.456**: The first three significant figures are 1, 2, and 3. The next digit is 4, which means we keep it the same. Thus, it becomes **123**. - **0.00098765**: The first three significant figures are 9, 8, and 7. The next digit is 6, which means we round up. Thus, it becomes **0.000988**. - **4567.89**: The first three significant figures are 4, 5, and 6. The next digit is 7, which means we round up. Thus, it becomes **4570**. 3. **Evaluating the Options**: - **A. 0.00457**: This is correct as it represents the number 0.00456789 rounded to three significant figures. - **B. 123**: This is also correct as it represents the number 123.456 rounded to three significant figures. - **C. 0.000988**: This is correct as it represents the number 0.00098765 rounded to three significant figures. - **D. 4570**: This is correct as it represents the number 4567.89 rounded to three significant figures. ### Conclusion All options A, B, C, and D are valid representations of the original numbers rounded to three significant figures. However, since the question asks for a single option, the most straightforward answer that directly corresponds to the original number with the least ambiguity is **A. 0.00457**. ### Summary - Significant figures include all non-zero digits and zeros between them. - Rounding to three significant figures involves looking at the first three significant digits and rounding based on the next digit. - The correct answer for the number rounded to three significant figures from the options provided is **A. 0.00457**. - All options represent valid rounding of their respective numbers, but A is the most straightforward answer.