Let the repeating decimal be (x)
Multiply (x) by a power of 10 so the repeating part lines up
Subtract the original equation from the new equation
Solve the resulting equation for (x)
Simplify the fraction if possible
For a pure repeating decimal like (0.overline{3}), use (10x=x) shifted one place
For a mixed repeating decimal like (0.1overline{6}), use different powers of 10 to move past the nonrepeating part and one full repeat
Write the final answer as a fraction in lowest terms