Reciprocal scaling with powers of 10: Given 1 ÷ 3.718 = 0.2689, find 1 ÷ 0.0003718 by relating the two denominators via powers of 10.

Introduction / Context:
Reciprocals of decimals are often connected by scaling denominators with powers of 10. Recognizing and using this relationship converts a new reciprocal into a simple multiple of a known one, saving time and effort.

Given Data / Assumptions:

• Known: 1 / 3.718 = 0.2689
• Find: 1 / 0.0003718

Concept / Approach:
Note that 0.0003718 = 3.718 × 10^-4. For any nonzero x and integer k, 1 / (x × 10^-k) = (1 / x) × 10^k. Apply this with x = 3.718 and k = 4.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 2.689: Misses the ×10^4 factor; only ×10^1.
• 26890: Over-scales by ×10^5.
• .2689: Uses the original reciprocal without scaling.

Common Pitfalls:

• Mistaking how many places the decimal shifts (four here).
• Applying the scaling to the numerator instead of to the reciprocal value.

Final Answer: