To evaluate the expression \(\frac{(2.813 \times 10^{-3} \times 1.063)}{(5.637 \times 10^{-2})}\) while reducing each number to two significant figures and leaving the final answer in two significant figures, we will follow these steps: ### Step 1: Round each number to two significant figures 1. **For \(2.813 \times 10^{-3}\)**: - The first two significant figures are 2 and 8. - Rounding gives us \(2.8 \times 10^{-3}\). 2. **For \(1.063\)**: - The first two significant figures are 1 and 0. - Rounding gives us \(1.1\). 3. **For \(5.637 \times 10^{-2}\)**: - The first two significant figures are 5 and 6. - Rounding gives us \(5.6 \times 10^{-2}\). ### Step 2: Substitute the rounded values into the expression Now we substitute the rounded values into the original expression: \[ \frac{(2.8 \times 10^{-3} \times 1.1)}{(5.6 \times 10^{-2})} \] ### Step 3: Calculate the numerator First, we calculate the numerator: \[ 2.8 \times 10^{-3} \times 1.1 = 3.08 \times 10^{-3} \] ### Step 4: Calculate the denominator The denominator is: \[ 5.6 \times 10^{-2} \] ### Step 5: Divide the numerator by the denominator Now we perform the division: \[ \frac{3.08 \times 10^{-3}}{5.6 \times 10^{-2}} = \frac{3.08}{5.6} \times \frac{10^{-3}}{10^{-2}} = \frac{3.08}{5.6} \times 10^{-1} \] ### Step 6: Calculate \(\frac{3.08}{5.6}\) Now we calculate \(\frac{3.08}{5.6}\): \[ \frac{3.08}{5.6} \approx 0.55 \] ### Step 7: Combine the results Now we combine this with \(10^{-1}\): \[ 0.55 \times 10^{-1} = 0.055 \] ### Step 8: Round the final answer to two significant figures Since we need to express our final answer in two significant figures, we round \(0.055\) to \(0.055\) (which is already in two significant figures). ### Conclusion Thus, the final answer is: **B. 0.055** ### Explanation of Other Options - **Option A (0.056)**: This is incorrect because it does not match our calculated value of \(0.055\). - **Option C (0.054)**: This is also incorrect as it is lower than our calculated value. - **Option D (0.54)**: This is incorrect because it is an order of magnitude higher than our calculated value. ### Revision Summary - Round each number to two significant figures before performing calculations. - Perform multiplication and division carefully, keeping track of significant figures. - Always express the final answer in the required number of significant figures. - Check calculations step-by-step to avoid common pitfalls in arithmetic.