Look at the repeating decimal. If the repeating decimal is one digit that repeats itself, as in .222222, place the repeating digit as the numerator over a denominator of 9, as in 2/9. This only works for a single digit that repeats itself. Check your work by dividing the numerator by the denominator of 9 to match it with the repeating decimal.
Convert repeating decimals with more than one digit that repeats, as in the decimal .1818. Count the number of repeating digits, of which there are two in the decimal .1818.
Multiply the given decimal by a power of 10 that has the same amount of zeros as the amount of digits that repeat. For example, multiply .1818 by 100 to account for the two repeating digits of 1 and 8. This places digits to the left of the decimal, giving you an answer with a whole number and decimal, as in 18.18.
Identify the repeating decimal to the right of the decimal as x, such as x = .1818 to use in an algebraic equation.
Create the equation. Write the value of 10 that you multiplied the decimal by next to the variable x, as in 100x. Follow this with an equal sign.
Write the whole number to the right of the equal sign, followed by an x to represent the decimal variable such as in 100x = 18 + x.
Subtract an x from each side of the equation to get the digit to the right of the equal sign alone. Rewrite the equation. For instance, 99x = 18.
Place both sides of the equation over the digit on the left side of the equal sign to get x alone and to find the fraction form of the repeating decimal, as in 99x/99 = 18/99.
Cancel out the numerator and denominator on the left side of the equation to make x equivalent to the right side fraction. For example, x = 18/99.
Reduce the fraction to simplest form by dividing by the greatest common factor. For instance, 18/99 ÷ 18 = 2/11.