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.
Aptitude
Decimal Fraction
Difficulty: Easy
Choose an option
-
A2689
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B2.689
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C26890
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D.2689
Answer
Correct Answer: 2689
Explanation
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:
0.0003718 = 3.718 × 10^-41 / 0.0003718 = (1 / 3.718) × 10^4= 0.2689 × 10000 = 2689Verification / Alternative check:
Direct calculator thinking: moving the decimal in the denominator four places right multiplies the reciprocal by 10^4.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:
2689