Evaluate a product/quotient of decimals efficiently Compute the exact value of 2 × [(3.6 × 0.48 × 2.50) / (0.12 × 0.09 × 0.5)].

Introduction / Context:
Large-looking decimal expressions often simplify cleanly when grouped strategically. This problem rewards rearranging factors and canceling early to avoid handling many zeros and decimal places at once.

Given Data / Assumptions:

• Expression: E = 2 × [(3.6 × 0.48 × 2.50) / (0.12 × 0.09 × 0.5)].
• All numbers are finite decimals; exact arithmetic is expected.

Concept / Approach:
Multiply the numerators and denominators in convenient pairs. Use the fact that 2.50 = 2.5 and 0.5 = 1/2 to simplify. Grouping as (3.6 × 0.48) first is neat because 36 × 48 has a well-known product pattern.

Step-by-Step Solution:
Compute numerator: 3.6 × 0.48 = 1.728.Then 1.728 × 2.5 = 4.32.Compute denominator: 0.12 × 0.09 = 0.0108.Then 0.0108 × 0.5 = 0.0054.Inside bracket: 4.32 / 0.0054 = 800.Multiply by the outside 2: E = 2 × 800 = 1600.

Verification / Alternative check:
Scale all numbers by powers of 10 to clear decimals (e.g., multiply top and bottom by 1000) and then cancel common factors. You will reach the same exact integer result 1600.

Why Other Options Are Wrong:
800 is the bracketed value before multiplying by 2; 500, 900, 600 come from partial or misgrouped computations.

Common Pitfalls:
Forgetting the outer factor 2; mishandling decimal places when multiplying or dividing; rounding mid-calculation instead of keeping exact values.

Final Answer:
1600