To determine which of the given numbers has three significant figures, we need to understand the concept of significant figures and how to identify them in different types of numbers. ### Definitions: - **Significant Figures**: These 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 count the significant figures. #### Option A: 0.00456 - **Step 1**: Identify the non-zero digits. Here, the digits "4", "5", and "6" are non-zero. - **Step 2**: Count the significant figures. The leading zeros (0.00) are not significant; they only serve to place the decimal point. Therefore, the significant figures are "4", "5", and "6". - **Conclusion**: This number has **3 significant figures**. #### Option B: 123.45 - **Step 1**: Identify the non-zero digits. All digits here (1, 2, 3, 4, and 5) are non-zero. - **Step 2**: Count the significant figures. Since there are no leading zeros and all digits are significant, this number has **5 significant figures**. - **Conclusion**: This number does not have 3 significant figures. #### Option C: 1001 - **Step 1**: Identify the non-zero digits. The digits "1", "0", "0", and "1" are present. - **Step 2**: Count the significant figures. The zeros here are between significant digits (1 and 1), so they are counted as significant. Therefore, this number has **4 significant figures**. - **Conclusion**: This number does not have 3 significant figures. #### Option D: 0.00230 - **Step 1**: Identify the non-zero digits. The digits "2" and "3" are non-zero. - **Step 2**: Count the significant figures. The leading zeros (0.00) are not significant. However, the trailing zero after "3" is significant because it indicates precision in the measurement. Thus, the significant figures are "2", "3", and the trailing "0". - **Conclusion**: This number has **3 significant figures**. ### Summary of Findings: - **Option A**: 0.00456 has 3 significant figures. - **Option B**: 123.45 has 5 significant figures. - **Option C**: 1001 has 4 significant figures. - **Option D**: 0.00230 has 3 significant figures. ### Correct Answer: Both **Option A (0.00456)** and **Option D (0.00230)** have three significant figures. However, if we are to select only one option, we can choose **Option A** as the first correct answer. ### Why Other Options Are Incorrect: - **Option B** is incorrect because it has 5 significant figures. - **Option C** is incorrect because it has 4 significant figures. - **Option D** is also correct, but if only one answer is to be selected, Option A is the first one listed. ### Revision Summary: - Significant figures include all non-zero digits, zeros between significant digits, and trailing zeros in decimal numbers. - Leading zeros are not counted as significant figures. - Both 0.00456 and 0.00230 have three significant figures, while 123.45 has five and 1001 has four. - When identifying significant figures, always start counting from the first non-zero digit.