To determine which decimal representation correctly approximates the fraction \( \frac{3}{8} \) to three significant figures, we first need to convert the fraction into its decimal form. ### Step 1: Convert the Fraction to Decimal To convert \( \frac{3}{8} \) into a decimal, we perform the division: \[ 3 \div 8 = 0.375 \] ### Step 2: Identify the Correct Option Now that we have the decimal representation of \( \frac{3}{8} \), which is \( 0.375 \), we can compare this with the options provided: - **A. 0.375** - **B. 0.38** - **C. 0.4** - **D. 0.370** ### Step 3: Analyze the Options 1. **Option A: 0.375** - This is the exact decimal representation of \( \frac{3}{8} \) and is accurate to three significant figures. The digits '3', '7', and '5' are all significant. 2. **Option B: 0.38** - This representation rounds \( 0.375 \) to two significant figures. While it is a close approximation, it does not meet the requirement of three significant figures. 3. **Option C: 0.4** - This representation rounds \( 0.375 \) to one significant figure. It is a very rough approximation and does not accurately reflect the value of \( \frac{3}{8} \). 4. **Option D: 0.370** - This representation has three significant figures, but it is not the correct value of \( \frac{3}{8} \). The correct value is \( 0.375 \), and \( 0.370 \) is less accurate. ### Conclusion The correct option that accurately represents \( \frac{3}{8} \) to three significant figures is: **A. 0.375** ### Summary of Why Other Options Are Incorrect - **B. 0.38**: Only two significant figures; does not meet the requirement. - **C. 0.4**: Only one significant figure; a very rough approximation. - **D. 0.370**: While it has three significant figures, it is not the correct value of \( \frac{3}{8} \). ### Revision Summary - The fraction \( \frac{3}{8} \) converts to the decimal \( 0.375 \). - The correct answer is **A. 0.375**, as it is the exact representation to three significant figures. - Options B, C, and D do not accurately represent \( \frac{3}{8} \) or do not meet the significant figure requirement. - Always ensure to check the number of significant figures when approximating values.