The correct option is **B. 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. Here’s how we can do that: 1. **Understanding the Fraction**: The fraction \( \frac{3}{8} \) means 3 parts out of 8 equal parts. To convert this into a decimal, we can perform the division of the numerator (3) by the denominator (8). 2. **Performing the Division**: - We divide 3 by 8. Since 3 is less than 8, we start by adding 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. So, the division process gives us \( 0.375 \). Therefore, \( \frac{3}{8} = 0.375 \). ### Why Option B is Correct - The decimal representation of \( \frac{3}{8} \) is exactly \( 0.375 \). This means that option B is the correct answer. ### Why the Other Options are Incorrect - **Option A: 0.35** - This value is less than \( 0.375 \). If we convert \( 0.35 \) back to a fraction, it would be \( \frac{35}{100} \) or \( \frac{7}{20} \), which is not equivalent to \( \frac{3}{8} \). - **Option C: 0.4** - This value is greater than \( 0.375 \). Converting \( 0.4 \) back to a fraction gives us \( \frac{4}{10} \) or \( \frac{2}{5} \), which is also not equivalent to \( \frac{3}{8} \). - **Option D: 0.5** - This value is significantly greater than \( 0.375 \). Converting \( 0.5 \) back to a fraction gives us \( \frac{5}{10} \) or \( \frac{1}{2} \), which is not equivalent to \( \frac{3}{8} \). ### Summary of Key Points - To convert a fraction to a decimal, divide the numerator by the denominator. - The fraction \( \frac{3}{8} \) converts to \( 0.375 \). - The other options (0.35, 0.4, and 0.5) do not equal \( \frac{3}{8} \) when converted back to fractions. - Always check your division steps carefully to avoid common pitfalls in decimal conversion.