Find the fourth proportional to 0.2, 0.12, and 0.3. (That is, 0.2 : 0.12 = 0.3 : x. Find x.)

Introduction / Context:
The fourth proportional x to a, b, c is defined by a : b = c : x. This yields x = (b * c) / a. With decimal values, careful multiplication and division are enough to get the exact result.

Given Data / Assumptions:

• a = 0.2
• b = 0.12
• c = 0.3

Concept / Approach:
Use x = (b * c) / a directly. No further transformation is required; just compute cleanly.

Step-by-Step Solution:
x = (0.12 * 0.3) / 0.2= 0.036 / 0.2= 0.18

Verification / Alternative check:
Check the proportion numerically: 0.2 : 0.12 = 5 : 3; with x = 0.18, 0.3 : 0.18 = 5 : 3 as well.

Why Other Options Are Wrong:
0.13 and 0.15 understate the correct division; 0.80 is unrelatedly large; 0.12 only repeats b and breaks the proportion.

Common Pitfalls:
Inverting the formula to x = (a * c)/b (incorrect), or losing decimal places during computation.

Final Answer:
0.18