The correct option is **B. 0.0046**. ### Step-by-Step Explanation: 1. **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 trailing zeros in the decimal part. - For the number 0.00456, we need to identify the significant figures. The leading zeros (the zeros before the first non-zero digit) are not counted as significant. Therefore, the significant figures in 0.00456 are 4, 5, and 6. 2. **Identifying the Significant Figures**: - The number 0.00456 has three significant figures: 4, 5, and 6. - When rounding to three significant figures, we need to consider the fourth digit to determine how to round the third digit. 3. **Rounding Process**: - The third significant figure in 0.00456 is 6 (the last digit we want to keep). - The next digit (the fourth significant figure) is 0. According to rounding rules, if the digit after the last significant figure is less than 5, we do not round up. If it is 5 or greater, we round up. - Since the fourth digit is 0, we do not round up the 6. Therefore, the rounded number remains 0.0046. 4. **Final Result**: - After rounding, we express the number in standard form, which is 0.0046. ### Why the Other Options Are Incorrect: - **A. 0.00456**: This option is incorrect because it does not round the number at all. We are specifically asked to round to three significant figures, and this option retains all five digits. - **C. 0.005**: This option is incorrect because it rounds the number too high. Rounding 0.00456 to three significant figures results in 0.0046, not 0.005. The digit 5 is not justified as the correct rounding. - **D. 0.0045**: This option is incorrect because it rounds down the last significant figure. The third significant figure is 6, and since the next digit is 0, we do not round down to 5. ### Common Pitfalls: - **Ignoring Leading Zeros**: Remember that leading zeros do not count as significant figures. Always start counting significant figures from the first non-zero digit. - **Rounding Rules**: Be careful with rounding rules. Always check the digit immediately after the last significant figure to determine whether to round up or keep it the same. ### Revision Summary: - Significant figures include all non-zero digits and zeros between them or after a decimal point. - To round a number, look at the digit immediately after the last significant figure. - For 0.00456, the third significant figure is 6, and the next digit is 0, so it rounds to 0.0046. - The correct answer is **B. 0.0046**.