(0.56% of 225) $\times$ (3.25% of 430) = $x$

### Concept & Strategy This problem tests your ability to handle the multiplication of two independent decimal-percentage expressions. The core concept is isolating the calculation into two distinct parts, simplifying each to a decimal, and then multiplying the final results. ### Step-by-Step Solution **Given:** * Part A: $0.56\%$ of $225$ * Part B: $3.25\%$ of $430$ **Calculation / Deduction:** * Solve Part A first. Convert the percentage to a fraction: $\frac{0.56}{100} \times 225 = 0.0056 \times 225$ * To multiply easily, think of it as $56 \times 225$ and then shift the decimal four places: $56 \times 225 = 12600$ Shift decimal 4 places left: $1.26$ * Solve Part B. Convert the percentage to a fraction: $\frac{3.25}{100} \times 430 = 0.0325 \times 430$ * Think of it as $325 \times 43$ and shift the decimal three places: $325 \times 43 = 13975$ Shift decimal 3 places left: $13.975$ * Multiply the two results (Part A $\times$ Part B): $1.26 \times 13.975$ * To perform this manually, calculate $126 \times 13975 = 1760850$. * Since $1.26$ has two decimal places and $13.975$ has three, the final answer needs five decimal places: $17.60850$, which is $17.6085$. ### Exam Strategy & Shortcut Use the unit digit and decimal placement to verify the options without doing the full massive multiplication. Look at the final step: $1.26 \times 13.975$. The last significant digits are $6$ and $5$. $6 \times 5 = 30$, so the final number (before trailing zeroes are dropped) ends in a $0$. $126 \times 13975$. We have $1 \times 13 \approx 13$, plus a quarter of $13$ is about $3$, so the answer must be around $16$ or $17$. Options C and D are in the $17$ range. Looking at exact digits requires the full math, but splitting $1.26$ into $(1 + \frac{1}{4})$ works wonderfully: $13.975 + \frac{13.975}{4} \approx 13.975 + 3.493 = 17.46$. Because $0.26$ is slightly larger than $0.25$, the answer must be slightly larger than $17.46$. The only option that fits is $17.6085$. ### Common Pitfall Losing track of decimal places during the final multiplication is the most common error. When multiplying $1.26$ by $13.975$, carefully count the decimal places in the factors ($2 + 3 = 5$) and apply them to the final integer product. ### Final Answer Therefore, the correct answer is **17.6085**.