To evaluate the expression \(\frac{(0.14^2 \times 0.275)}{7(0.02)}\) and find the correct answer among the options provided, we will break down the calculation step-by-step. ### Step 1: Calculate \(0.14^2\) First, we need to square \(0.14\): \[ 0.14^2 = 0.14 \times 0.14 \] Calculating this: \[ 0.14 \times 0.14 = 0.0196 \] ### Step 2: Multiply by \(0.275\) Next, we multiply the result from Step 1 by \(0.275\): \[ 0.0196 \times 0.275 \] To perform this multiplication, we can break it down: \[ 0.0196 \times 0.275 = 0.0196 \times \frac{275}{1000} = \frac{0.0196 \times 275}{1000} \] Calculating \(0.0196 \times 275\): \[ 0.0196 \times 275 = 5.390 \] Now, dividing by \(1000\): \[ \frac{5.390}{1000} = 0.00539 \] ### Step 3: Calculate the denominator \(7(0.02)\) Now, we calculate the denominator \(7(0.02)\): \[ 7 \times 0.02 = 0.14 \] ### Step 4: Divide the results Now we can divide the result from Step 2 by the result from Step 3: \[ \frac{0.00539}{0.14} \] To perform this division, we can convert \(0.14\) to a fraction: \[ 0.14 = \frac{14}{100} = \frac{7}{50} \] Thus, we can rewrite the division as: \[ \frac{0.00539}{0.14} = 0.00539 \div 0.14 = 0.00539 \times \frac{100}{14} \] Calculating \(0.00539 \times \frac{100}{14}\): First, calculate \(\frac{100}{14}\): \[ \frac{100}{14} \approx 7.142857 \] Now multiply: \[ 0.00539 \times 7.142857 \approx 0.0384 \] ### Step 5: Round to three decimal places Now we round \(0.0384\) to three decimal places: \[ 0.0384 \approx 0.038 \] ### Conclusion The final answer is \(0.038\), which corresponds to option D. ### Explanation of Other Options - **Option A (0.039)**: This is incorrect because our calculation showed that the result is \(0.0384\), which rounds to \(0.038\), not \(0.039\). - **Option B (0.385)**: This is incorrect as it is significantly larger than our calculated value. It does not relate to the operations performed. - **Option C (0.033)**: This is also incorrect as it is less than our calculated value. It does not reflect the multiplication and division performed. ### Revision Summary - To evaluate expressions, perform operations step-by-step, ensuring accuracy at each stage. - Always round your final answer to the required number of decimal places. - Be cautious with multiplication and division, especially with decimals. - Check each option against your calculated result to confirm correctness.