Decimal multiplication — compute exactly Evaluate 10.8 × 5.5 × 8.4 and report the exact product.

Introduction / Context:
Accurate decimal multiplication benefits from breaking the task into manageable parts and accounting for decimal places at the end or by stagewise multiplication.

Given Data / Assumptions:

• Compute P = 10.8 × 5.5 × 8.4.
• Standard decimal arithmetic applies.

Concept / Approach:
Multiply two factors at a time, then multiply the result by the third. Keep track of decimal placement or do integer multiplication with scaled factors.

Step-by-Step Solution:
First pair: 10.8 × 5.5 = (10.8 × 5) + (10.8 × 0.5) = 54 + 5.4 = 59.4.Then multiply by 8.4: 59.4 × 8 = 475.2 and 59.4 × 0.4 = 23.76.Sum: 475.2 + 23.76 = 498.96.

Verification / Alternative check:
Use integer scaling: 108 × 55 × 84 = 498960; adjust by 4 decimal places total → 498.96.

Why Other Options Are Wrong:
489.96 and 485.69 come from partial products or misplaced decimals; 458.69 and 509.86 are miscalculations.

Common Pitfalls:
Forgetting to include the 0.5 part of 5.5, or misplacing decimal points after the final multiplication.

Final Answer:
498.96