How to change a recurring decimal to a fraction

How do you convert a recurring decimal into a fraction?

For example, convert .333 to a fraction.

Follow these steps to convert the recurring decimal to a fraction

Step 1:

Set up an equation by setting x equal the repeating decimal you are trying to convert to a fraction.

This is equation one.
Step 2:
Set up a second equation in which the repeating decimal is to the left of the decimal point. This is equation two.

In order to do this, you will have to multiply x by a factor of 10

Step 3:
Subtract equation one from equation 2
Step 4:
Solve for x

Step 5:


Example problems

Example 1. Change .666 to fraction form.
Step 1. X = .6666
Step 2.
In order to have the repeating decimal to the left of the decimal, you need to move the decimal one place to the right.

Remember, what you do to one side of the equation you must perform on both sides.

Multiply both sides by 10

10x = 6.666

Step 3. Subtract equation 1 from equation 2
10x = 6.66

   X = 0.666
____________

9x = 6

Step 4. Solve for x

9x = 6

9   = 9

X = 6/9 which equals ⅔
Example 2
Convert the decimal .1616….. to a fraction
Step 1. X = .1616
Step 2. 10x = 16.1616…
Step 3.
100x = 16.1616

- x   = .1616

____________

99x = 16

Step 4.

99x = 16

99       99

X = 16/99

Step 5

Simplify the fraction

16 / 9 = 2

99/ 9 = 11

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