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, any zeros between significant digits, and any trailing zeros in the decimal portion. ### Analyzing Each Option Let's analyze each option one by one to see which one is correctly rounded to three significant figures. #### Option A: 0.004567 - **Identifying Significant Figures**: The leading zeros (0.00) are not significant. The significant figures start from the first non-zero digit, which is 4. Therefore, the significant figures are 4, 5, and 6. - **Rounding to Three Significant Figures**: The number rounded to three significant figures is 0.00457 (the fourth digit is 6, which rounds the 6 up). - **Conclusion**: This option is correctly rounded to three significant figures. #### Option B: 123.456 - **Identifying Significant Figures**: All digits are significant here (1, 2, 3, 4, 5, 6). - **Rounding to Three Significant Figures**: The first three significant figures are 1, 2, and 3. The number rounded to three significant figures is 123 (the fourth digit is 4, which does not round the 3 up). - **Conclusion**: This option is also correctly rounded to three significant figures. #### Option C: 78.91011 - **Identifying Significant Figures**: All digits are significant (7, 8, 9, 1, 0, 1, 1). - **Rounding to Three Significant Figures**: The first three significant figures are 7, 8, and 9. The number rounded to three significant figures is 79.0 (the fourth digit is 1, which does not round the 9 up). - **Conclusion**: This option is correctly rounded to three significant figures. #### Option D: 0.00034567 - **Identifying Significant Figures**: The leading zeros are not significant. The significant figures start from the first non-zero digit, which is 3. Therefore, the significant figures are 3, 4, 5. - **Rounding to Three Significant Figures**: The number rounded to three significant figures is 0.000346 (the fourth digit is 6, which rounds the 5 up). - **Conclusion**: This option is correctly rounded to three significant figures. ### Summary of Findings - **All options (A, B, C, D)** are correctly rounded to three significant figures. ### Final Answer Since all options are correctly rounded, the answer is that **all options (A, B, C, D) are correct**. ### Revision Summary - Significant figures include all non-zero digits, zeros between significant digits, and trailing zeros in decimals. - Rounding involves looking at the digit immediately after the last significant figure to determine if you round up or keep it the same. - All given options were analyzed, and each was found to be correctly rounded to three significant figures. - Always remember to ignore leading zeros when counting significant figures.