
Shortcut Trick
Each numerator term is exactly 10 × its corresponding denominator term.
Ratio: 0.05 / 0.005 = 10, 0.41 / 0.041 = 10, 0.073 / 0.0073 = 10.
Since the terms are squared, the ratio of squares is 102 = 100.
Expression = 100 × [Sum of squares in Denominator] / [Sum of squares in Denominator].
Simplifying the fraction gives a final value of 100.
∴ The correct option is C.

Alternate Method
Given: Expression = [(0.05)2 + (0.41)2 + (0.073)2] / [(0.005)2 + (0.041)2 + (0.0073)2]
Formula Used: (k × a)2 = k2 × a2
⇒ 0.05 = 10 × 0.005
⇒ 0.41 = 10 × 0.041
⇒ 0.073 = 10 × 0.0073
⇒ Numerator = (10 × 0.005)2 + (10 × 0.041)2 + (10 × 0.073)2
⇒ Numerator = 100 × [(0.005)2 + (0.041)2 + (0.0073)2]
⇒ Expression = {100 × [(0.005)2 + (0.041)2 + (0.073)2]} / [(0.005)2 + (0.041)2 + (0.0073)2]
⇒ Expression = 100
∴ The correct option is C.

Additional Information
Powers of Decimals
When a number is multiplied by 10n, the decimal point shifts n places to the right. Squaring such a number results in a multiplier of 102n.
Algebraic Scaling
For any non-zero expression, (k2x + k2y + k2z) / (x + y + z) = k2, provided the denominator sum is not zero.
Common Ratios in Fractions
If each corresponding term in the numerator and denominator has the same ratio r, then the ratio of their sums is also r.