3. $8,218 \overline{6}=$

Step 1 ：Set the repeating decimal as a variable x: \(x = 8.218\overline{6}\)

Step 2 ：Multiply x by 10 to shift the decimal point one place to the right: \(10x = 82.186\overline{6}\)

Step 3 ：Subtract the original x from the shifted x: \(10x - x = 82.186\overline{6} - 8.218\overline{6}\)

Step 4 ：Solve for x: \(9x = 73.968\) and \(x = \frac{7396}{1000}\)

Step 5 ：Separate the whole number and the fraction: \(x = 8 + \frac{396}{1000}\)

Step 6 ：Simplify the fraction: \(x = 8 + \frac{2}{5}\)

Step 7 ：Combine the whole number and the simplified fraction: \(x = \frac{40}{5} + \frac{2}{5}\)

Step 8 ：Final Answer: \(\boxed{x = \frac{42}{5}}\)