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.

Set up a second equation in which the repeating decimal is to the left

**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

**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.

10x = 6.66

Convert the decimal .1616….. to a fraction

100x = 16.1616

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 210x = 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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