To determine the correct decimal representation of the fraction \(\frac{3}{8}\) rounded to two decimal places, we will follow a step-by-step approach. ### Step 1: Convert the Fraction to Decimal To convert the fraction \(\frac{3}{8}\) into a decimal, we perform the division of the numerator (3) by the denominator (8). \[ 3 \div 8 = 0.375 \] ### Step 2: Rounding to Two Decimal Places Now that we have the decimal representation \(0.375\), we need to round it to two decimal places. Rounding involves looking at the third decimal place to decide how to round the second decimal place. - The second decimal place in \(0.375\) is \(7\). - The third decimal place is \(5\). According to rounding rules: - If the digit in the third decimal place is 5 or greater, we round up the second decimal place. - If it is less than 5, we leave the second decimal place as it is. Since the third decimal place is \(5\), we round up the \(7\) in the second decimal place: \[ 0.375 \text{ rounded to two decimal places is } 0.38. \] ### Conclusion: Correct Option Thus, the correct decimal representation of the fraction \(\frac{3}{8}\) rounded to two decimal places is: **C. 0.38** ### Explanation of Other Options Now, let’s analyze the other options to understand why they are incorrect: - **A. 0.36**: This option is incorrect because it is less than the actual value of \(0.375\). Rounding down to \(0.36\) does not follow the rounding rules since \(0.375\) rounds up to \(0.38\). - **B. 0.37**: This option is also incorrect. While it is closer to \(0.375\) than \(0.36\), it still does not round correctly. The second decimal place should be rounded up from \(7\) to \(8\) due to the \(5\) in the third decimal place. - **D. 0.39**: This option is incorrect as it rounds up too much. The correct rounding of \(0.375\) does not reach \(0.39\); it only goes up to \(0.38\). ### Summary of Key Points - The fraction \(\frac{3}{8}\) converts to the decimal \(0.375\). - Rounding \(0.375\) to two decimal places results in \(0.38\) because the third decimal place is \(5\). - The correct answer is **C. 0.38**. - Other options (A, B, D) do not follow the rounding rules correctly. This thorough understanding of the conversion and rounding process will help you tackle similar problems in the future!