1. The problem is to find the decimal value of the fraction $\frac{1}{39}$.\n\n2. The formula to convert a fraction to a decimal is to divide the numerator by the denominator: $$\text{Decimal} = \frac{\text{Numerator}}{\text{Denominator}}$$\n\n3. Here, the numerator is 1 and the denominator is 39, so we perform the division: $$1 \div 39$$\n\n4. Performing the division, we get a repeating decimal: $$\frac{1}{39} = 0.025641025641...$$\n\n5. This decimal repeats the sequence "025641" indefinitely.\n\n6. Therefore, the exact decimal representation is $$0.\overline{025641}$$\n\nFinal answer: $$\frac{1}{39} = 0.\overline{025641}$$