The correct option for the decimal representation of the fraction \( \frac{3}{8} \) rounded to two significant figures is **B. 0.38**. ### Step-by-Step Explanation: 1. **Convert the Fraction to Decimal:** To convert the fraction \( \frac{3}{8} \) into a decimal, we perform the division of 3 by 8. \[ 3 \div 8 = 0.375 \] 2. **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 any trailing zeros in the decimal portion. In our case, we need to round \( 0.375 \) to two significant figures. 3. **Rounding to Two Significant Figures:** The number \( 0.375 \) has three significant figures (3, 7, and 5). To round it to two significant figures, we look at the third significant figure, which is 5. According to rounding rules, if the digit following the last significant figure (in this case, the second significant figure, which is 7) is 5 or greater, we round up. - The second significant figure is 7. - The third significant figure is 5. Since the third figure is 5, we round up the second figure (7) by 1, resulting in: \[ 0.375 \rightarrow 0.38 \] 4. **Final Result:** Therefore, the decimal representation of \( \frac{3}{8} \) rounded to two significant figures is **0.38**. ### Explanation of Other Options: - **A. 0.37:** This option is incorrect because it rounds down instead of up. The correct rounding of 0.375 should lead to 0.38, not 0.37. - **C. 0.39:** This option is incorrect because it incorrectly rounds up the second significant figure too much. The correct rounding of 0.375 does not lead to 0.39. - **D. 0.40:** This option is incorrect as it suggests rounding up to a whole number, which is not appropriate for 0.375. The correct rounding leads to 0.38, not 0.40. ### Common Pitfalls: - **Misunderstanding Significant Figures:** Students often confuse rounding rules or do not recognize how many significant figures are required. - **Rounding Up Incorrectly:** Some may round up when the next digit is less than 5, which is not correct. - **Ignoring Decimal Places:** It’s important to focus on the significant figures rather than just the decimal places. ### Revision Summary: - To convert a fraction to a decimal, divide the numerator by the denominator. - Rounding to significant figures requires looking at the digit immediately after the last significant figure. - If that digit is 5 or greater, round up; if it’s less than 5, round down. - The correct rounding of \( 0.375 \) to two significant figures is \( 0.38 \).