1. State the problem: Calculate $0.02^3 \times 10^{-1}$.\n\n2. Calculate $0.02^3$: Since $0.02 = \frac{2}{100} = \frac{1}{50}$, we have \n$$0.02^3 = \left(\frac{1}{50}\right)^3 = \frac{1}{50^3} = \frac{1}{125000} = 8 \times 10^{-6}.$$\n\n3. Multiply this result by $10^{-1}$: \n$$8 \times 10^{-6} \times 10^{-1} = 8 \times 10^{-7}.$$\n\n4. Final answer: \n$$0.02^3 \times 10^{-1} = 8 \times 10^{-7}.$$