To determine which of the given numbers is expressed with the correct number of significant figures when rounded to three significant figures, we need to analyze each option carefully. ### Step-by-Step Analysis **Significant Figures Overview:** - 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 trailing zeros only when there is a decimal point. - When rounding to a specific number of significant figures, we keep that many digits and round the last digit based on the digit that follows it. **Options Analysis:** **A. 0.004567** - The significant figures in this number are 4, 5, 6, and 7. The leading zeros (0.00) are not significant. - When rounded to three significant figures, we look at the first three non-zero digits: 4, 5, and 6. The next digit is 7, which means we round up. - Thus, 0.004567 rounded to three significant figures is **0.00457**. - **Significant Figures Count:** 3 (correct). **B. 123.456** - All digits in this number are significant. - When rounding to three significant figures, we take the first three digits: 1, 2, and 3. The next digit is 4, which means we do not round up. - Thus, 123.456 rounded to three significant figures is **123**. - **Significant Figures Count:** 3 (correct). **C. 9870** - The significant figures in this number are 9, 8, and 7. The trailing zero (0) is ambiguous without a decimal point; it may or may not be significant. - When rounding to three significant figures, we take 9, 8, and 7. The next digit is 0, which means we do not round up. - Thus, 9870 rounded to three significant figures is **9870** (but it is ambiguous whether the trailing zero is significant). - **Significant Figures Count:** 3 (ambiguous). **D. 0.07080** - The significant figures in this number are 7, 0, 8, and the trailing 0 (because there is a decimal point). - When rounding to three significant figures, we take 7, 0, and 8. The next digit is 0, which means we do not round up. - Thus, 0.07080 rounded to three significant figures is **0.0708**. - **Significant Figures Count:** 4 (not correct). ### Conclusion The correct option that is expressed with the correct number of significant figures when rounded to three significant figures is **B. 123.456**. ### Why Other Options Are Incorrect or Weaker: - **A. 0.004567**: While it can be rounded to three significant figures, it is not the only correct option. - **C. 9870**: The ambiguity of the trailing zero makes it less clear whether it has three significant figures. - **D. 0.07080**: This has four significant figures, which does not meet the requirement of three significant figures. ### Revision Summary: - Significant figures include all non-zero digits, zeros between significant digits, and trailing zeros in decimal numbers. - Rounding involves keeping the specified number of significant figures and adjusting based on the next digit. - Ambiguity in trailing zeros can affect the interpretation of significant figures. - The correct answer for three significant figures in this case is **B. 123.456**.