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 of the decimal point. This is equation two.

**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.

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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MooMooMath and Science upload a new math or science video every day. We have over 1400 math and science videos to help in school and life.

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