# Decimals to fractions worksheet pdf: Grade 6 Math Worksheet: Converting decimals to fractions

Posted on## 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.

Fahim Shahriyar

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.

## Fractions and Decimals Class 7 Extra Questions Maths Chapter 2

**Extra Questions for Class 7 Maths Chapter 2 Fractions and Decimals**

#### Fractions and Decimals Class 7 Extra Questions Very Short Answer Type

Question 1.

If \(\frac { 2 }{ 3 }\) of a number is 6, find the number.

Solution:

Let x be the required number.

Hence, the required number is 9.

Question 2.

Find the product of \(\frac { 6 }{ 7 }\) and 2\(\frac { 2 }{ 3 }\).

Solution:

Question 3.

Solve the following:

Solution:

Question 4.

Multiply 2.05 and 1.3.

Solution:

#### Fractions and Decimals Class 7 Extra Questions Short Answer Type

Question 5.

Solve the following:

(a) 3 – \(\frac { 2 }{ 3 }\)

(b) 4 + \(\frac { 2 }{ 5 }\)

Solution:

Question 6.

Arrange the following in ascending order:

Solution:

Question 7.

Find the products:

(i) 2.4 × 100

(ii) 0.24 × 1000

(iii) 0.024 × 10000

Solution:

Question 8.

Arnav spends 1\(\frac { 3 }{ 4 }\) hours in studies, 2\(\frac { 1 }{ 2 }\) hours in playing cricket. How much time did he spend in all?

Solution:

Time spent by Arnav in studies = 1\(\frac { 3 }{ 4 }\) hours

Time spent by Arnav in playing cricket = 2\(\frac { 1 }{ 2 }\) hours

Total time spent by Arnav = 1\(\frac { 3 }{ 4 }\) hours + 2\(\frac { 1 }{ 2 }\) hours

Question 9.

A square paper sheet has 10\(\frac { 2 }{ 5 }\) cm long side. Find its perimeter and area.

Solution:

Question 10.

Solution:

Question 11.

The product of two numbers is 2.0016. If one of them is 0.72, find the other number.

Solution:

Product of two numbers = 2.0016

One number = 0.72

Other number = 2.0016 ÷ 0.72

Hence, the required number = 2.78.

Question 12.

Reemu reads \(\frac { 1 }{ 5 }\)th pages of a book. If she reads further 40 pages, she would have read \(\frac { 7 }{ 10 }\)th

page of the book. How many pages are left to be read? [NCERT Exemplar]

Solution:

Let the total number of pages be x.

Number of pages read by Reemu = \(\frac { 1 }{ 5 }\)x

If she reads 40 more pages,

Total number of pages read by her = \(\frac { 1 }{ 5 }\)x + 40

Question 13.

\(\frac { 1 }{ 8 }\) of a number equals \(\frac { 2 }{ 5 }\) ÷ \(\frac { 1 }{ 20 }\). What is the number? (NCERT Exemplar)

Solution:

Let the number be x.

Hence, the required number = 64.

Question 14.

Simplify the following:

Solution:

Question 15.

The weight of an object on the Moon is \(\frac { 1 }{ 6 }\) its weight on the Earth. If an object weight 5\(\frac { 3 }{ 5 }\) kg on the Earth. How much would it weight on the Moon? [NCERT Exemplar]

Solution:

Question 16.

A picture hall has seats for 820 persons. At a recent film show, one usher guessed it was \(\frac { 3 }{ 4 }\) full, another that it was \(\frac { 2 }{ 3 }\) full. The ticket office reported 648 sales. Which usher (first or second) made the better guess? [NCERT Exemplar]

Solution:

Total number of seats = 820

Number of ticket sold = 648

For first usher = \(\frac { 3 }{ 4 }\) × 648 = 3 × 162 = 486

For second usher = \(\frac { 2 }{ 3 }\) × 648 = 2 × 216 = 432

Since 432 < 486

Hence, the first usher guessed better.

##### Extra Questions for Class 7 Maths

##### NCERT Solutions for Class 7 Maths

## (PDF) April 1a April 29 Literary Shenteryakova S.

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T. Sobakina.

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Yakhina F.R. Funny poems for children I.

Tokmakova, K. Chukovskogo,

Pivovarova, O. Grigoryeva, T.

Sobakina

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to answer questions. Reading

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Introduction of new vocabulary.

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Charles Perrault «Puss in Boots».

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link to the worksheet of the lesson

2c April 29 mathematics Kapkanova O.N. Multiplying the number 2.

Multiplication by 2.

link to the lesson worksheet

April 29 English Somova O.I. English alphabet link to lesson worksheet

April 3a April 29 Danilina E.F. General questions in Present

Simple

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3a April 29 English Somova O. I. Animals link to lesson worksheet

3a April 29 mathematics Uchaeva N.A. Methods of oral calculations

types: 240 * 4, 203 * 4, 960:3.

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horizontal target. Jumping rope

.

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3b April 29 Russian Kuznetsova L.V. Control dictation No. 4 with

grammar task

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3b April 29, mathematics Kuznetsova L.V. Methods of oral calculations

types: 240•4, 203•4, 960:3.

reference to worksheet

3b April 29 literary

reading

Kuznetsova L.V. Yu.I. Ermolaev

“Let go”

link to worksheet

3b April 29 physical education Kuznetsova L. V. Station exercises.

Pulling up

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3b April 29 Kuznetsova L.V. In the north of Europe. link to worksheet

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grammar task).

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3c April 29 mathematics Znamenskaya A.G. Work on mistakes. Methods

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link to lesson 9 worksheet0003

3c April 29 literary

reading

Znamenskaya A.G. Yu.I. Ermolaev

«Let go.»

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3c April 29 English Somova O.I. Imperative mood link to the worksheet of the lesson

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4a April 29 Russian Yusupova T.V. Exercise in recognizing

verb conjugations according to

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link to worksheet

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Change the trial digit.

link to worksheet

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meals

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verb endings

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4b April 29 the world around Zubova E.V. Great war and great

Victory

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link to the worksheet of the lesson

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5a April 29 technology Odintsov N.P. Assembly of products from

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wire, artificial materials

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art.0002 5а 29 April literature Terentyeva OV

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sheet metal,

wire, artificial

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link to the lesson worksheet

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wire, artificial materials

link to the worksheet of the lesson

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verbs link to lesson worksheet

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Robert Lewis Stevenson

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link to the lesson worksheet

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link to the worksheet of the lesson

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on the coordinate line

link to the worksheet of the lesson

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start. Counter relay.

link to the lesson sheet

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Modal verb should

link to lesson worksheet Moscow and Tver: struggle for leadership

link to the worksheet of the lesson

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on the coordinate line

link to the worksheet of the lesson

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equivalent to

link to lesson 9 worksheet0003

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R/R Story based on

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6c April 29 literature Terentyeva O. V.

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7a 29 April. Physical

culture.

Zubailov I.Sh. The concept of exercise rhythm. Link to worksheet.

7a April 29 English Moshnyaga I.A. At the doctor’s appointment link to lesson worksheet

7b April 29 Russian Kapinskaya L.V. Distinguishing particles and prefixes

not

link to the worksheet of the lesson

7b April 29 German Danilina E.F. In a healthy body — a healthy

spirit

link to lesson worksheet

7b April 29 Geography Fomina G.G. Eastern Europe link to lesson worksheet

7b April 29 Physics Sizemov B.A. Efficiency of the mechanism (solving

problems)

link to the worksheet of the lesson

7b April 29 Vinokurova algebra S.A. Solving problems using

linear equations

link to the lesson worksheet

7b April 29 English Karakina I.R. Longevity Secrets Link to Lesson 9 Worksheet0003

7b April 29 Medvedev’s story I.V. Church schism link to lesson worksheet

7b April 29 Informatics Makushin A. M. computer presentations link to the lesson worksheet

7c April 29 geometry Rodina V.A Construction of a triangle by

three elements

link to the lesson worksheet

7c April 29 Russian Andreeva L.V. Shaping particles link to lesson worksheet

7c April 29 Geography Fomina G.G. Southern Europe link to lesson 9 worksheet0003

7c April 29 Physics Sizemov B.A. Efficiency of the mechanism (solving

tasks)

link to the worksheet of the lesson

7c April 29. Physical

culture.

Zubailov I.Sh. The concept of exercise rhythm. Link to worksheet.

7c April 29 fine art

Igoshina M.V. The garden of my dreams link to the worksheet of the lesson

8a April 29 Emphasis marks

punctuation for introductory

words, constructions

link to lesson worksheet

https://yadi.sk/i/TnRlEOVOyLxcNw

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900 02 https://yadi.sk/ i/oe1cLnEd-zct1Q

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8a April 29 German Danilina E .F. Interesting cities in Germany

(part I)

link to the worksheet of the lesson

8a April 29 Vinokurov Algebra SA Problem solving with

systems of rational

equations

link to the lesson worksheet

8a April 29 English Karakina I.R. Generalization on the topic

«Outstanding people of the world»

link to the worksheet of the lesson

8a April 29 biology Muromtseva Yu. V. Internal structure

Reptiles

link to lesson worksheet

8b April 29 literature Davydova L.V. Punctuation marks for

introductory words and insertions

constructions

link to the worksheet of the lesson

8b Solving problems using

systems of rational

equations

link to the lesson worksheet

8b 29.04.2020 Physical culture

Athletics. Low start.

Start run.

link to the lesson sheet

8b April 29 social science Medvedeva I.V. Consumption link to lesson 9 worksheet0003

8b April 29 biology Muromtseva Yu.V. Internal structure

Reptiles

link to the worksheet of the lesson

8c April 29 algebra Vinokurov SA. Solving systems of rational

equations in other ways.

Solving problems using

systems of rational

equations

link to the worksheet of the lesson . Athletics. Low start.

Start run.

link to the lesson sheet

8c April 29 social science Medvedeva I. V. Consumption link to lesson worksheet

8c April 29 biology Muromtseva Yu.V. Internal structure

Preventers

Link to a work sheet lesson

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9a April 29 geometry Rodina V.A Parallel transfer link to the worksheet of the lesson

9a April 29 OBZh Glukhov A.A. Concepts of HIV infection and

AIDS.

link to lesson worksheet

April 29 German

(second foreign language

)

Karakina I. R. Defense of the project “One day

without a computer and home appliances

”

link to the lesson worksheet

9a April 29 English Pronina V.V. Phrasal verb Link to lesson worksheet

April 29 Russian Davydova L.V. Repetition. Preparation for the OGE link to the worksheet of lesson

9a April 22 Lvov’s story L.N. The final period of

revolutions.

link to lesson worksheet

9a April 29 biology Muromtseva Yu.V. Visual analyzer link to lesson worksheet

9b April 29 geometry Rodina VA Parallel transfer link to lesson worksheet

9b April 29 OBZh Glukhov A.A. Concepts of HIV infection and

AIDS.

link to the lesson worksheet

9b April 29 German Danilina E.F. Media discussion link to lesson 9 worksheet0003

9b April 29 Russian Davydova L.V. Repetition. Preparation for the OGE link to the worksheet of the lesson

9b April 29, physics Sizemov B.A. Repetition: Thermal phenomena

2

link to the lesson worksheet

9b April 29 English Pronina V. V. Word formation (conversion) link to lesson worksheet

9b April 29 biology Muromtseva Yu.V. Visual analyzer link to lesson worksheet

9c April 29 OBZh Glukhov A.A. Concepts of HIV infection and

AIDS.

link to the worksheet of the lesson Project protection. Presentation

of the project

link to the lesson worksheet

9c April 29 physicist Sizemov B.A. Review: Thermal phenomena

2

link to lesson worksheet

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9th April 29 English Moshnyaga I.A. Verbs to get, to be. link to lesson worksheet

9c April 29 English Pronina V.V. The use of complex

additions

link to the worksheet of the lesson

April 22 Lvov’s history LN State and society at the turn of the century

.

link to the lesson worksheet

9c April 22 social science Lvova LN. Repetition. link to lesson 9 worksheet0003

9c April 29 biology Muromtseva Yu.V. Visual analyzer link to lesson worksheet

April 10a April 29 Mathematician V.A. Rodina The simplest trigonometric equations

link to lesson worksheet Drilling training link to lesson worksheet

10a April 29 geography Fomina G.G. Territorial structure

cities

link to lesson worksheet

10a April 29 project by Fomin G. G. Conducting experimental

experimental work

link to the worksheet of the lesson

10a April 29 Medvedeva IV The right to a favorable environment

link to the worksheet of the lesson

10a April 29 biology Muromtseva Yu.V. Gamatogenesis. Fertilization link to lesson worksheet

April 11a April 29 Mathematics Rodina V.A Preparation for the Unified State Examination. Decision

KIM.

link to the lesson worksheet

11a April 29 literature Andreeva L.V. «Mother’s Yard». Man —

a righteous person, a bearer of the people’s

morality, kindness,

unselfishness, diligence.

link to lesson worksheet

April 11a Geography Fomina G.G. Foreign Europe link to the worksheet of the lesson Athletics. Low start.

Start run.

link to the lesson sheet

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