$47.7 \times 12.4 \times 8.6 = $x$

Concept & Formula The problem requires basic decimal multiplication. The key insight is to count the total number of decimal places in the factors to determine the correct decimal placement in the final product. Step-by-Step Solution * First, ignore the decimals and multiply the numbers as integers: $477 \times 124 \times 86$. * Let's group them: $477 \times 124 = 59148$. * Now multiply by 86: $59148 \times 86 = 5086728$. * Count the total decimal places in the original problem: $47.7$ (1 place), $12.4$ (1 place), and $8.6$ (1 place). Total = 3 decimal places. * Place the decimal point 3 positions from the right in the product: $5086.728$. Exam Strategy & Shortcut Use digital root and unit digit analysis to save time. Unit digit of the integers: $7 \times 4 = 28$ (ends in 8). $8 \times 6 = 48$ (ends in 8). The exact answer must end in 8. This eliminates option (d). Next, use approximation: $50 \times 12 \times 9 = 5400$. The answer must be reasonably close to 5400. Doing a slightly closer rough calculation ($48 \times 12 \approx 576$; $576 \times 8.5 \approx 4896$) points clearly to option (a). Common Pitfall Students often misplace the decimal point by adding digits incorrectly or by messing up the large integer multiplication. Always double-check by estimating the magnitude ($50 \times 12 \times 8 = 4800$) to ensure your decimal is in the right spot. Final Answer **Therefore, the correct answer is 5086.728.**