Cube root of a very small decimal: Find the cube root of 0.000027.

Introduction / Context:
We need the cube root of a small decimal. Recognize familiar cubes: 27 is 3^3, so 0.000027 relates directly to a scaled cube.

Given Data / Assumptions:

• Number: 0.000027 = 27 / 10^6.
• Use principal cube root (positive).

Concept / Approach:
For positive a, ∛(a/10^n) = ∛a / 10^(n/3) when n is a multiple of 3. Here n = 6 is divisible by 3, which makes evaluation straightforward.

Step-by-Step Solution:

Verification / Alternative check:
(0.03)^3 = 27 / 10^6 = 0.000027, confirming the result exactly.

Why Other Options Are Wrong:

• .3^3 = 0.027, too large by a factor of 1000.
• .003^3 = 2.7e-8, far too small.
• “None of these” is not needed since .03 is present.

Common Pitfalls:
Mixing square-root logic with cube roots or miscounting decimal-place triplets for cube roots.

Final Answer:
.03