**Correct Option: A. 0.375** ### Step-by-Step Explanation To determine which decimal representation is equivalent to the fraction \( \frac{3}{8} \), we need to convert the fraction into its decimal form. This can be done through division. 1. **Understanding the Fraction**: The fraction \( \frac{3}{8} \) means we have 3 parts out of a total of 8 equal parts. 2. **Performing the Division**: To convert \( \frac{3}{8} \) into a decimal, we divide 3 by 8. - Set up the division: \( 3 \div 8 \). - Since 3 is less than 8, we can add a decimal point and a zero to 3, making it 30. - Now, we divide 30 by 8: - 8 goes into 30 three times (since \( 8 \times 3 = 24 \)). - Subtract 24 from 30, which gives us 6. - Bring down another 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 another 0, making it 40. - 8 goes into 40 five times (since \( 8 \times 5 = 40 \)). - Subtract 40 from 40, which gives us 0. - Therefore, the result of the division \( 3 \div 8 \) is \( 0.375 \). 3. **Final Result**: Thus, \( \frac{3}{8} = 0.375 \). ### Why the Other Options are Incorrect - **Option B: 0.4** - This decimal represents \( \frac{4}{10} \) or \( \frac{2}{5} \). It is greater than \( \frac{3}{8} \) because \( 0.4 \) is equivalent to \( 0.5 \) when compared to \( 0.375 \). - **Option C: 0.5** - This decimal represents \( \frac{5}{10} \) or \( \frac{1}{2} \). It is also greater than \( \frac{3}{8} \) since \( 0.5 \) is equivalent to \( 0.500 \), which is larger than \( 0.375 \). - **Option D: 0.625** - This decimal represents \( \frac{625}{1000} \) or \( \frac{5}{8} \). It is greater than \( \frac{3}{8} \) because \( 0.625 \) is equivalent to \( 0.625 \), which is larger than \( 0.375 \). ### Summary of Key Points - To convert a fraction to a decimal, divide the numerator by the denominator. - \( \frac{3}{8} \) converts to \( 0.375 \) through long division. - The other options (0.4, 0.5, and 0.625) do not equal \( \frac{3}{8} \) and are larger than \( 0.375 \). ### Revision Summary - **Fraction to Decimal**: Divide the numerator by the denominator. - **Correct Conversion**: \( \frac{3}{8} = 0.375 \). - **Comparison**: Other options (0.4, 0.5, 0.625) are greater than \( 0.375 \). - **Long Division**: Practice long division for converting fractions to decimals for better understanding.