You may not always know that you're going to get an answer with a repeating decimal when you begin long division. Let's say we're converting the common fraction 1/3 to a decimal. Just set it up with the 3, or the denominator, outside the division bracket, and the 1 inside the division bracket.
 Since your answer will be less than one, this will help you put the answer in decimal form. You should also place a decimal point after the "1" inside the division bracket.
 Now, to do long division, you'll begin by making the "1." into a "1.0" so you can divide "3" into what you can think of as the number "10." Here's where you go from there:


Simply divide 10 by 3. You'll get 3 x 3, or 9, with a remainder of 1. So, write a 3 after the "0." above the division bracket, and subtract the answer, 9, from 10 to get a remainder of 1.
Add another "0" after the "1" below the "10" to get "10" again. When you divide "3" into "10" again, you'll have to repeat the process, placing another "3" after the first "3" above the division bracket along with subtracting another "9" from the new "10" you have left.
Keep going until you notice a pattern. Notice something funny yet? You'll see that this can go on forever. You can keep dividing 3 into 10, getting a remainder of 1, and writing yet another "3" after the decimal point above the division bracket.
 Now that you see that the "3" can repeat forever, simply write your answer as ".3" with a bar over the "3" to indicate that it will repeat forever, or as ".33" with the same bar over both numbers. This is 1/3 in decimal form because you'll never be able to get a perfect, clean decimal out of it.


There are many fractions that have repeating decimals, such as 2/9 (".2" repeating), 5/6 (".83" with the "3" repeating), or 7/9 (".7" repeating). This will happen any time you have a denominator that is a multiple of 3 with a numerator that won't go into it cleanly.
Set up the long-division problem.
Place a zero with a decimal point after it above the division bracket.
Do long division.
Write your answer.
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