1. **State the problem:** We need to calculate the value of $\frac{0.208}{0.8}$.\n\n2. **Formula used:** Division of decimals is performed by dividing the numerator by the denominator.\n\n3. **Convert to fraction:** Write the division as a fraction: $$\frac{0.208}{0.8}$$\n\n4. **Eliminate decimals:** Multiply numerator and denominator by 1000 to remove decimals: $$\frac{0.208 \times 1000}{0.8 \times 1000} = \frac{208}{800}$$\n\n5. **Simplify the fraction:** Find the greatest common divisor (GCD) of 208 and 800, which is 16.\n\n6. **Divide numerator and denominator by 16:** $$\frac{\cancel{208}^{13}}{\cancel{800}^{50}}$$\n\n7. **Final simplified fraction:** $$\frac{13}{50}$$\n\n8. **Convert to decimal:** $$\frac{13}{50} = 0.26$$\n\n**Answer:** $0.26$