### Correct Option: A. 0.375 ### Detailed Explanation: To convert the fraction \( \frac{3}{8} \) into its decimal equivalent, we can perform the division of the numerator (3) by the denominator (8). 1. **Perform the Division**: - Divide 3 by 8. - Since 3 is less than 8, we start with 0. - We can express this as \( 3.000 \) (adding decimal places). - Now, we divide: - 8 goes into 30 three times (since \( 8 \times 3 = 24 \)). - Subtract 24 from 30, which gives us 6. - Bring down the next 0 (making it 60). - 8 goes into 60 seven times (since \( 8 \times 7 = 56 \)). - Subtract 56 from 60, which gives us 4. - Bring down the next 0 (making it 40). - 8 goes into 40 five times (since \( 8 \times 5 = 40 \)). - Subtract 40 from 40, which gives us 0. Thus, the division results in \( 0.375 \). 2. **Rounding to Three Significant Figures**: - The result \( 0.375 \) is already in three significant figures (the digits 3, 7, and 5). - Therefore, no further rounding is necessary. ### Why Other Options Are Incorrect: - **Option B: 0.380** - This option suggests that the decimal equivalent is \( 0.380 \). However, this is incorrect because it implies an additional significant figure that does not exist in the original fraction. The correct decimal representation is \( 0.375 \), and rounding it to three significant figures does not change it. - **Option C: 0.400** - This option indicates that the decimal equivalent is \( 0.400 \). This is incorrect as it suggests that the value is larger than \( 0.375 \). The fraction \( \frac{3}{8} \) does not round up to \( 0.400 \) because it is less than \( 0.4 \). - **Option D: 0.370** - This option suggests that the decimal equivalent is \( 0.370 \). This is incorrect because it is less than \( 0.375 \). The correct value is \( 0.375 \), and rounding down to \( 0.370 \) would misrepresent the value of the fraction. ### Summary of Key Points: - The decimal equivalent of \( \frac{3}{8} \) is \( 0.375 \). - The conversion involves simple division, resulting in \( 0.375 \) without the need for rounding. - Each digit in \( 0.375 \) is significant, making it three significant figures. - Other options either misrepresent the value or incorrectly suggest additional or fewer significant figures. This thorough understanding of converting fractions to decimals and rounding will help you in similar problems in your exams.