Recognize uniform decimal scaling in sums of squares: Compute [(0.05)^2 + (0.41)^2 + (0.073)^2] / [(0.005)^2 + (0.041)^2 + (0.0073)^2] using powers-of-10 relationships.

Introduction / Context:This problem checks whether you can see patterns in decimal scaling. The denominator terms are each precisely one-tenth of the corresponding numerator terms, and squaring magnifies that scaling in a predictable way. Exploiting this pattern yields the answer instantly.

Given Data / Assumptions:

• Numerator: (0.05)^2 + (0.41)^2 + (0.073)^2.
• Denominator: (0.005)^2 + (0.041)^2 + (0.0073)^2.

Concept / Approach:If x is scaled to x/10, then (x/10)^2 = x^2/100. Since every denominator term is the square of a numerator term divided by 10, each denominator square equals the corresponding numerator square divided by 100. Thus the whole denominator is 1/100 of the numerator sum, and the ratio is 100.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 0.1, 10, 1000: Each assumes an incorrect scaling factor (1/10, 10, or 1000) rather than 100.

Common Pitfalls:

• Forgetting that the square of a tenth is a hundredth.
• Adding before recognizing the uniform scaling wastes time and risks arithmetic slips.

Final Answer: