Repeating s can be quite daunting, especially when you are faced with the need to them into s. However, the process of converting decimals into fractions is easier than you think. In this article, we will take you through the step-by-step process of converting any repeating decimal into a fraction.

Step 1: Identify the repeating decimal

The first step in converting a repeating decimal into a fraction is to identify that it is repeating. A repeating decimal is a decimal that has a pattern of digits that repeat infinitely. For example, 0.6666666… is a repeating decimal because the 6 repeats infinitely.

Step 2: Assign variables

The next step is to assign variables to the repeating part of the decimal. The variable should be the sequence of digits that repeat. For example, if the decimal is 0.33333…, the variable would be represented by the repeating digits “33”.

Step 3: Write the equation

To convert a repeating decimal into a fraction, you need to write an equation that includes the variable you identified in step 2. For example, if the decimal is 0.33333…, the equation would be:

x = 0.33333…
10x = 3.33333…

Step 4: Eliminate the repeating decimal

The next step is to eliminate the repeating decimal. You can do this by subtracting the equation in step 1 from the equation in step 2. In this example, you would subtract x from 10x as shown below:

10x – x = 3.33333… – 0.33333…

Step 5: Solve for x

Once the repeating decimal has been eliminated, you can solve for x. In the example above, the equation becomes:

9x = 3

x = 3/9

Step 6: Simplify the fraction

The last step in converting a repeating decimal into a fraction is to simplify the fraction. In our example, we can simplify 3/9 to 1/3. Therefore, the repeating decimal 0.33333… can be expressed as the fraction 1/3.

Here’s another example to illustrate the method:

Convert 0.63636363… into a fraction

Step 1: Identify the repeating decimal

The repeating digits in this decimal are “63”.

Step 2: Assign variables

x = 0.63636363…

Step 3: Write the equation

x = 0.63636363…
100x = 63.636363…

Step 4: Eliminate the repeating decimal

100x – x = 63.636363… – 0.63636363…

99x = 63

Step 5: Solve for x

x = 63/99

Step 6: Simplify the fraction

We can simplify 63/99 to 7/11. Therefore, the repeating decimal 0.63636363… can be expressed as the fraction 7/11.

Conclusion

In conclusion, converting a repeating decimal into a fraction may seem daunting at first, but it is a simple process. The key is to identify the repeating decimal, assign variables, write the equation, eliminate the repeating decimal, solve for x and simplify the fraction. With practice, you will become more adept at converting repeating decimals into fractions.

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