Find the mean proportional (geometric mean) between 0.32 and 0.02.

Introduction / Context:The mean proportional (geometric mean) m between two positive numbers a and b satisfies a : m = m : b, or m^2 = a * b. Hence m = sqrt(a * b). Compute accurately with decimals.

Given Data / Assumptions:

• a = 0.32
• b = 0.02
• m^2 = a * b ⇒ m = sqrt(0.32 * 0.02)

Concept / Approach:Multiply the two decimals and take the square root. Keep precision to avoid rounding errors that might push you toward a nearby option.

Step-by-Step Solution:Product = 0.32 * 0.02 = 0.0064m = sqrt(0.0064) = 0.08

Verification / Alternative check:Check proportion: 0.32 : 0.08 = 4 : 1 and 0.08 : 0.02 = 4 : 1; proportions match, confirming m.

Why Other Options Are Wrong:0.34 and 0.30 are far too large; 0.16 would be m^2, not m; 0.06 does not satisfy the proportion check.

Common Pitfalls:Confusing arithmetic mean with geometric mean; forgetting to take the square root after multiplying.

Final Answer:0.08