Since x must be a positive integer, both sides of the inequality can be multiplied by \(x^3\)

\(\frac{2}{x^3} < 0.02\)

\(2 < 0.02x^3\)

\(200 < 2x^3\)

\(100 < x^3\)

\(x^3 > 100\)

In the resulting inequality, the least positive integer value for x is 5.

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