# Free Converting Repeating Decimals to Fractions Worksheet

Hey, little champs! Have you ever faced difficulties while converting repeating decimals to fractions? If the answer is yes then we are here to rescue you. Today, we are going to learn the ins and outs of **converting repeating decimals to fractions worksheet**.

Converting a simple decimal is quite easy. But when it comes to converting repeating decimals to fractions, it follows up a different process. In this article, we will explore the method for converting repeating decimals to fractions and provide examples and practice problems to help you master this fundamental math skill.

There is also a pdf of converting repeating decimals to fractions worksheet. Download them and Enjoy!

## Repeating Decimals to Fractions Worksheet: Facts and Examples

**Repeating decimals** follow a repetitive sequence after the decimal point. The repetitive values can be converted into fractions form. You may be aware of **converting fractions to decimals** also. Here we have discussed converting repeating decimals to fractions worksheet.

A “**terminating decimal**” can be converted to a fraction by counting the finite number of digits that follow the decimal point, then multiplying and dividing by the corresponding power of ten.

**Example**: 0.25= (0.25✕100)/100= 25⁄100=1/4

It is quite simple to convert decimals into fractions. But what about repetitive decimals? The number of decimal places with repeated decimals is limitless, so it is impossible for us to count the repetitive numbers.

**Examples of repeating decimals:**

0.45454545…….

9.5555555……

15.356356356…..

The above examples show us the repetitive decimals. Let’s jump into the stepwise procedure to convert the repeating decimals to fractions.

### Facts and Charts of Repeating Decimals to Fractions

We have made a chart for different types of repeating decimals to their corresponding fractions form. It will give you a better visualization of the methods. By reading the chart you will get an idea of converting repeating decimals to fractions worksheet.

## How to Convert Repeating Decimals to Fractions: Learn with Steps!

Suppose, you want to convert 0.55555….to fractions. Follow the below steps to do so.

** Step 1**: Assume the given decimal number to “x”.

So, we assume x=0.55555….____________(1)

** Step 2**: Here, the repetitive digit is

**5**. The number of repetitive digits is

**1**.

** Step 3**: After ensuring the repeating digits come after the decimal point, multiply both sides of the equation by a power of ten equal to the number of repeating digits.

As we have one repetitive digit, we will multiply equation (1) with 10.

10x=0.55555….✕10

10x=5.5555……____________(2)

** Step 4**: At this moment, subtract equation (1) from equation (2).

We will get, 10x-x=5.5555…..- 0.55555…..

From the above equation, we will solve for “x”.

9x=5.

x=5/9.

## 3 Interactive Ways of Converting Decimals to Fractions

There are different kind of decimals which has repetitive digits. We differentiate them into three categories. You may have single, multiple, or mixed digits for converting repeating decimals to fractions worksheet.

### Single Repeating Digit Conversion

Suppose, you want to convert 0.77777….=0.7 to fractions. Following the below steps you can convert this single repeating digit.

** Step 1**: Assume the given decimal number to “x”.

So, we assume x=0.77777….____________(1)

** Step 2**: Here, the repetitive digit is

**7**. The number of repetitive digits is

**1**.

** Step 3**: After ensuring the repeating digits come after the decimal point, multiply both sides of the equation by a power of ten equal to the number of repeating digits. As we have one repetitive digit, we will multiply equation (1) with 10. 10x=0.77777….✕10

10x=7.7777……____________(2)

** Step 4**: At this moment, subtract equation (1) from equation (2).

We will get, 10x-x=7.7777…..- 0.77777…..

From the above equation, we will solve for “x”.

9x=7.

x=7/9

It is the worksheet pdf of converting repeating decimals to fractions worksheet for single recurring digits.

### Multiple Repeating Digit Conversion

Now, we will convert multiple repeating decimals to fractions. Let’s do it. Suppose, we want to convert 4.181818….

** Step 1**: Assume the given decimal number to “x”.

So, we assume x=4.181818….____________(1)

** Step 2**: Here, the repetitive digit is

**18**. The number of repetitive digits is

**2**.

** Step 3**: After ensuring the repeating digits come after the decimal point, multiply both sides of the equation by a power of ten equal to the number of repeating digits. Here, the repetitive digit is

**2**. So, we will multiply both sides with

**10²=100.**100x=4.181818….✕100

100x=418.181818……____________(2)

** Step 4**: At this moment, subtract equation (1) from equation (2). We will get, 100x-x=418.181818………..- 4.181818….

From the above equation, we will solve for “x”.

99x= 414.

x=414/99

This is the pdf for converting repeating decimals to fractions worksheet for multiple repeating digits.

### Mixed Digits Conversion (Repetitive and Non-repetitive)

You may face problems when it comes to solving mixed digits where you have both repetitive and non-repetitive digits. Suppose, you want to convert 8.9525252…. To fractions.

** Step 1**: Assume the given decimal number to “x”. So, we assume x=8.9525252….____________(1)

** Step 2**: Here, the repetitive digit is

**52**. The number of repetitive digits is

**2**and the only non-repetitive digit is

**9**.

** Step 3**: So, we will multiply both sides with 10³=1000 as there are

**2**repetitive digits and

**1**non-repetitive digit. 1000x=8.9525252….✕1000

1000x=8952.525252……____________(2)

Here, the non-repetitive digit is **3**. So, we will multiply both sides with the power of 10.

10x=8.9525252….✕10

10x=89.525252…..____________(3)

** Step 4**: Now, subtract equation (3) from equation (2).

We will get, 1000x-10x=8952.525252….- 89.525252…..

From the above equation, we will solve for “x”.

990x= 8863.

x=8863/990.

Here is the pdf file for converting repeating decimals to fractions worksheet of mixed type digits.

## Repeating Decimal to Fraction Conversion: Tips & Tricks

We know what are you looking for. Are there any tricks to convert decimals to fractions, Right? Guess what! You can convert the decimals to fractions without following the steps described above. Follow the tricks for converting decimals to fractions worksheet.

**Decimal type 1****: 0.xyz**

This trick is suitable only when the repetitive digit is **1**. The formula for converting this kind of number is

0.xyz=(Repeated digit or digit)/(Number of 9’s equal to the number of repeated digits)

**Example 1**: 0.66666…..=0.6 Here, the repetitive digit is 6.

So, the fraction= 6/9

= 2/3.

**Example 2**: 0.323232….=0.32 Here, the repetitive digits are 32.

So, the fraction= 32/99

**Decimal type 2****: **0. xy…..vw

In the following types, there are some non-repeating digits also.

So, the formula will be 0.xy…..vw=(xyvw-xy)/(Number of 9’s equal to the repetitive digits and Number of 0’s for the non-repetitive terms)

**Example 1**: 0.4525252…

Here, the repetitive digits are 52 and the non-repetitive digit is 4.

So, the fraction=(452-4)/990

=448/990

=224/445

**Example 2**: 5.25979797…

Here, the repetitive digits are **97** and the non-repetitive digits are **525**.

So, the fraction=(52597-525)/9900

=52072/9900

=13018/2475.

## Download Practice Worksheet PDF

So, that’s all about today. We have discussed **3** different types of repeating decimals and converted them to fractions. Whether you are a student or a professional, understanding how to convert repeating decimals to fractions will enable you to perform calculations more accurately and efficiently.

The free converting repeating decimals to fractions worksheet PDF is available for download below. You can download this practice sheet by clicking on the download button and printing it from your device.

If you have any queries regarding this article, feel free to knock us through comments. Your feedback is valuable to us.

Welcome to my blog. I am Fahim Shahriyar Dipto. Currently, I am working as a content developer in You Have Got This Math. I will post math-related articles here from now on. I have completed my bachelor’s degree in Mechanical Engineering from BUET. So, I am a mechanical graduate with a lot of interest in research and exploring new work. I always try to think of something creative and innovative. So, I choose to write creative content here.