$32.4 \times 11.5 \times 8.5 = $x$

Concept & Formula This is a continuous decimal multiplication problem. When multiplying decimals, multiply the numbers as if they were integers, then place the decimal point so the product has the same number of decimal places as the sum of decimal places in the factors. Step-by-Step Solution * Treat the numbers as integers: $324$, $115$, and $85$. * Multiply the first two: $324 \times 115 = 37260$. * Multiply the result by the third: $37260 \times 85 = 3167100$. * Count the total decimal places in the given expression: 1 + 1 + 1 = 3 decimal places. * Apply the decimal point to the product: $3167.100$. * Drop the trailing zeros: $3167.1$. Exam Strategy & Shortcut Calculate the unit digit of the non-zero integer components. Look at $32.4 \times 11.5 = 372.6$. The trailing zero was dropped. Next multiply $372.6 \times 8.5$. The last digit before the decimal will end based on $6 \times 5 = 30$, meaning it ends in a single decimal place `.1` (from the integer math $3726 \times 85$). Looking at the options, (b) and (c) end in .1. Estimating $30 \times 11 \times 8 = 2640$ helps confirm magnitude, pushing us toward (c). Common Pitfall Forgetting to drop trailing zeros after placing the decimal point, which leads to confusion when matching the calculated answer ($3167.100$) with the given simplified options ($3167.1$). Final Answer **Therefore, the correct answer is 3167.1.**