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**: - **Option A: 0.004567** - 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, 6, and 7. This number has **4 significant figures**. - **Option B: 12345** - All digits in this number are non-zero, so they are all significant. Thus, the significant figures are 1, 2, 3, 4, and 5. This number has **5 significant figures**. - **Option C: 789.1** - All digits are non-zero, and the digit 1 is also significant. Therefore, the significant figures are 7, 8, 9, and 1. This number has **4 significant figures**. - **Option D: 0.05678** - The leading zeros (0.00) are not significant. The significant figures start from the first non-zero digit, which is 5. Therefore, the significant figures are 5, 6, 7, and 8. This number has **4 significant figures**. 2. **Determine Which Number is Rounded to Three Significant Figures**: - After analyzing all options, we see that none of the numbers listed (A, B, C, or D) are rounded to three significant figures. They all have either 4 or 5 significant figures. ### Conclusion Since none of the options provided are rounded to three significant figures, the correct answer is that **none of the options (A, B, C, D) are correct**. ### Explanation of Why Other Options Are Wrong or Weaker - **Option A (0.004567)**: Has 4 significant figures, not 3. - **Option B (12345)**: Has 5 significant figures, not 3. - **Option C (789.1)**: Has 4 significant figures, not 3. - **Option D (0.05678)**: Has 4 significant figures, not 3. ### Common Pitfalls - **Ignoring Leading Zeros**: Many students mistakenly count leading zeros as significant figures. - **Miscounting Digits**: It's easy to miscount the number of significant figures, especially in larger numbers or those with decimals. - **Confusing Trailing Zeros**: Remember that trailing zeros in a whole number without a decimal point are not significant, while trailing zeros in a decimal are. ### Revision Summary - Significant figures include all non-zero digits, zeros between significant digits, and trailing zeros in decimals. - Leading zeros are not counted as significant figures. - None of the provided options (A, B, C, D) are rounded to three significant figures; they all have 4 or 5 significant figures. - Always double-check your counting of significant figures to avoid common mistakes.