Compute the exact product: 503 × 201 = ?

Introduction: Even in an approximation section, sometimes exact multiplication is expected. Use distributive expansion to keep the arithmetic simple and error-free, especially when one factor is just over a round hundred or thousand.

Given Data / Assumptions:

• Compute 503 × 201 exactly.
• Both numbers are close to “round” decompositions.

Concept / Approach: Expand 201 as (200 + 1) or 503 as (500 + 3). Apply the distributive property: (a + b)(c + d) = ac + ad + bc + bd. This avoids long multiplication and reduces mental load.

Step-by-Step Solution:

Verification / Alternative check: Alternatively, (500 + 3)(200 + 1) = 500*200 + 500*1 + 3*200 + 3 = 100000 + 500 + 600 + 3 = 101103. Same result confirms correctness.

Why Other Options Are Wrong: 101100 is near but off by 3; 110000 and 100003 are far; 100500 is a mid-way distractor but incorrect.

Common Pitfalls: Dropping small cross terms (like 3*200 or 500*1). Keep every term from the expansion to avoid small but fatal errors.

Final Answer: 101103