Approximation and quick calculation: Evaluate 26.823 × 27.923 × 4.5001 and select the closest option (use sensible rounding/estimation where appropriate).

Introduction / Context:
This approximation problem tests number sense and the ability to round sensibly to get a near-exact product quickly. By grouping close-to-integer factors and using small adjustments, you can arrive at a highly accurate estimate without long multiplication.

Given Data / Assumptions:

• Expression: 26.823 * 27.923 * 4.5001
• Answer choices are coarse (hundreds-level), so a near-integer rounding is appropriate.
• Select the closest option to the true value.

Concept / Approach:
Round each factor to a convenient nearby value, compute, and then refine if needed. Because options are spaced by 50–400, rounding to 27, 28, and 4.5 or using a tighter pair like 26.8 and 27.9 still lands very close to the exact product. Use compensations only if choices are close together.

Step-by-Step Solution:

Verification / Alternative check:
Use midpoint method: (26.823 * 27.923) ≈ 27.373 * 27.373 ≈ 749.3; then 749.3 * 4.5001 ≈ 3371.9. Again, closest to 3400.

Why Other Options Are Wrong:

• 3500 and 3450: Slightly high versus the refined estimate near 3370.
• 3100: Too low given both partial estimates.
• None of these: A reasonable close option exists (3400).

Common Pitfalls:
Over-rounding one factor too far (e.g., 30) without compensating others can push the product well above the true range. Keep rounding balanced across factors.

Final Answer:
3400