The correct option is **C. 4.560**. ### Detailed Explanation: **Understanding Significant Figures:** Significant figures (or significant digits) 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 the Number 0.004560:** 1. **Leading Zeros:** The number 0.004560 has leading zeros (the zeros before the first non-zero digit, which is 4). These leading zeros are not counted as significant figures. They merely indicate the position of the decimal point. 2. **Non-Zero Digits:** The digits 4, 5, and 6 are all non-zero and are therefore counted as significant figures. 3. **Trailing Zeros in Decimal:** The trailing zero (the last zero after the 6) is significant because it comes after a decimal point and follows non-zero digits. This indicates the precision of the measurement. **Counting the Significant Figures in 0.004560:** - The significant figures in 0.004560 are: - 4 (1 significant figure) - 5 (1 significant figure) - 6 (1 significant figure) - 0 (the trailing zero after 6, which is significant) Thus, the total number of significant figures in 0.004560 is **4**. ### Why Option C is Correct: - **C. 4.560** has 4 significant figures: - The digits 4, 5, 6 are significant, and the trailing zero after the 6 is also significant because it indicates precision. Therefore, it correctly represents the number of significant figures in the original number. ### Why the Other Options are Incorrect: - **A. 4:** This option only counts the digit 4 as significant. It ignores the significant figures contributed by the 5, 6, and the trailing zero. Thus, it is incorrect. - **B. 4.56:** This option counts only the digits 4, 5, and 6, but it does not include the trailing zero, which is significant in the context of the original number. Therefore, it is also incorrect. - **D. 0.00456:** This option has the same digits as the original number but does not include the trailing zero. The leading zeros are not significant, and it only counts 3 significant figures (4, 5, and 6). Thus, it is incorrect. ### Summary: - Significant figures include all non-zero digits, zeros between them, and trailing zeros in decimal numbers. - The number 0.004560 has 4 significant figures: 4, 5, 6, and the trailing zero. - The correct representation of this number with the correct number of significant figures is **C. 4.560**. - Options A, B, and D fail to account for all significant figures present in the original number. ### Revision Summary: - Significant figures are crucial for indicating precision in measurements. - Leading zeros are not significant; trailing zeros after a decimal point are significant. - The number 0.004560 has 4 significant figures: 4, 5, 6, and the trailing zero. - The correct answer is C. 4.560, as it accurately reflects the significant figures of the original number.