Multiplication by 625 — Power-of-10 Trick Compute 6674 × 625 quickly by using 625 = 10^4 / 16.

Introduction / Context:
Mental math with numbers like 25, 125, and 625 benefits from rewriting them as fractions of powers of 10. Since 625 = 5^4 = 10000 / 16, you can multiply by 10000 (add four zeros) and then divide by 16, which is efficient and accurate.

Given Data / Assumptions:

• We need 6674 × 625.
• Use 625 = 10000 / 16.
• All operations are in base-10 decimal arithmetic.

Concept / Approach:
Compute 6674 × 10000 first (easy place-value shift), then perform an exact division by 16. Division by 16 can be done by successive halving: divide by 2 four times.

Step-by-Step Solution:
1) Multiply: 6674 × 10000 = 66,740,000.2) Divide by 2: 33,370,000.3) Divide by 2 again (÷4 total): 16,685,000.4) Divide by 2 again (÷8 total): 8,342,500.5) Divide by 2 again (÷16 total): 4,171,250.

Verification / Alternative check:
Long multiplication or a calculator yields the same product 4,171,250, confirming the power-of-10 trick is valid.

Why Other Options Are Wrong:
Other choices stem from halving errors or misplacing zeros during the 10000 multiplication step.

Common Pitfalls:
Forgetting that four halvings are required to divide by 16; dropping a zero when scaling by 10000; arithmetic slips during repeated division.

Final Answer:
4171250