Converting recurring decimals to fractions is a crucial skill in ... Show more
Sign up to see the contentIt's free!
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Responding to change (a2 only)
Energy transfers (a2 only)
Infection and response
Homeostasis and response
Cell biology
Biological molecules
Organisation
Substance exchange
The control of gene expression (a2 only)
Bioenergetics
Genetic information & variation
Inheritance, variation and evolution
Genetics & ecosystems (a2 only)
Ecology
Cells
Show all topics
1f industrialisation and the people: britain, c1783-1885
Medieval period: 1066 -1509
Britain & the wider world: 1745 -1901
2d religious conflict and the church in england, c1529-c1570
1l the quest for political stability: germany, 1871-1991
The cold war
1c the tudors: england, 1485-1603
Inter-war germany
2m wars and welfare: britain in transition, 1906-1957
2j america: a nation divided, c1845-1877
World war two & the holocaust
2n revolution and dictatorship: russia, 1917-1953
2s the making of modern britain, 1951-2007
World war one
Britain: 1509 -1745
Show all topics
27
0
Ruby Kilpatrick
06/10/2025
Maths
Recurring decimals to fractions study notes for GCSE Maths Foundation and Higher!
1,209
•
6 Oct 2025
•
Ruby Kilpatrick
@rubykilpatrick
Converting recurring decimals to fractions is a crucial skill in ... Show more
This page provides a detailed example of how to convert a recurring decimal to a fraction, a common topic in Recurring Decimals GCSE questions and answers. The process is broken down into six clear steps, making it an excellent resource for students working on recurring decimals to fractions worksheets.
The example used is 0.738̅, which is a recurring decimal where the 8 repeats indefinitely. The method shown can be applied to various recurring decimals to fractions examples, making it a versatile technique for GCSE maths.
Definition: A recurring decimal is a decimal number where a digit or group of digits repeats indefinitely after the decimal point.
Step 1 involves setting the recurring decimal equal to a variable x. This is the foundation for the algebraic approach used in this method.
Example: Let x = 0.738̅
Step 2 requires multiplying both sides of the equation by 10 for each non-recurring decimal place. In this case, there are two non-recurring decimal places (7 and 3), so we multiply by 10.
Highlight: 10x = 7.38̅
Step 3 involves multiplying both sides by 10 for each recurring decimal place. Here, only the 8 is recurring, so we multiply by 100.
Example: 1000x = 738.38̅
Step 4 is crucial as it involves subtracting the equations from steps 2 and 3. This clever step cancels out the recurring part of the decimal.
Highlight: 1000x - 10x = 738.38̅ - 7.38̅
Step 5 solves for x by simplifying the equation from step 4.
Example: 990x = 731
Step 6, the final step, involves simplifying the fraction if possible. In this case, the fraction 731/990 is already in its simplest form.
Vocabulary: Simplest form means that the numerator and denominator have no common factors other than 1.
This method can be applied to various recurring decimals to fractions questions, making it an essential skill for GCSE maths. Students can practice with a recurring decimals to fractions worksheet or use a recurring decimals to fractions calculator to check their work.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
App Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
Ruby Kilpatrick
@rubykilpatrick
Converting recurring decimals to fractions is a crucial skill in GCSE maths questions. This guide provides a step-by-step approach to solve such problems, which is particularly useful for those seeking Recurring Decimals to Fractions maths genie answersor working... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
This page provides a detailed example of how to convert a recurring decimal to a fraction, a common topic in Recurring Decimals GCSE questions and answers. The process is broken down into six clear steps, making it an excellent resource for students working on recurring decimals to fractions worksheets.
The example used is 0.738̅, which is a recurring decimal where the 8 repeats indefinitely. The method shown can be applied to various recurring decimals to fractions examples, making it a versatile technique for GCSE maths.
Definition: A recurring decimal is a decimal number where a digit or group of digits repeats indefinitely after the decimal point.
Step 1 involves setting the recurring decimal equal to a variable x. This is the foundation for the algebraic approach used in this method.
Example: Let x = 0.738̅
Step 2 requires multiplying both sides of the equation by 10 for each non-recurring decimal place. In this case, there are two non-recurring decimal places (7 and 3), so we multiply by 10.
Highlight: 10x = 7.38̅
Step 3 involves multiplying both sides by 10 for each recurring decimal place. Here, only the 8 is recurring, so we multiply by 100.
Example: 1000x = 738.38̅
Step 4 is crucial as it involves subtracting the equations from steps 2 and 3. This clever step cancels out the recurring part of the decimal.
Highlight: 1000x - 10x = 738.38̅ - 7.38̅
Step 5 solves for x by simplifying the equation from step 4.
Example: 990x = 731
Step 6, the final step, involves simplifying the fraction if possible. In this case, the fraction 731/990 is already in its simplest form.
Vocabulary: Simplest form means that the numerator and denominator have no common factors other than 1.
This method can be applied to various recurring decimals to fractions questions, making it an essential skill for GCSE maths. Students can practice with a recurring decimals to fractions worksheet or use a recurring decimals to fractions calculator to check their work.
Our AI Companion is a student-focused AI tool that offers more than just answers. Built on millions of Knowunity resources, it provides relevant information, personalised study plans, quizzes, and content directly in the chat, adapting to your individual learning journey.
You can download the app from Google Play Store and Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.
27
Smart Tools NEW
Transform this note into: ✓ 50+ Practice Questions ✓ Interactive Flashcards ✓ Full Mock Exam ✓ Essay Outlines
Explore effective techniques for multiplying decimals, including step-by-step calculations and the importance of decimal placement. This summary covers key concepts such as handling decimal points, examples of multiplication with decimals, and tips for accurate results. Ideal for students looking to master decimal multiplication.
Explore essential mathematical concepts including percentage calculations, fractions, decimals, and their applications in real-world scenarios. This summary covers key formulas for appreciation, depreciation, perimeter, area, volume, and probability, making it a valuable resource for National 5 Maths students.
Enhance your skills in multiplication and division with this comprehensive GCSE arithmetic practice. This resource covers key operations including adding and multiplying decimals, as well as division methods. Perfect for exam preparation, it includes a variety of questions with clear instructions and marks allocation. Ideal for students aiming to improve their mathematical proficiency.
This summary covers the essential concepts of ordering decimals and understanding place value. Learn how to compare decimal numbers, convert between decimals, fractions, and percentages, and the significance of each digit's place value. Ideal for students looking to enhance their numeracy skills in mathematics.
Explore the essential techniques for adding, subtracting, multiplying, and dividing decimals. This comprehensive guide covers key concepts such as aligning decimal points, handling zeroes, and converting between fractions, decimals, and percentages. Ideal for students in years 5 to 8, this resource provides clear examples and step-by-step instructions to enhance your understanding of decimal operations.
Explore effective methods for dividing and multiplying decimals with clear examples. This summary covers essential techniques and provides step-by-step guidance to enhance your understanding of decimal division. Ideal for students seeking to master decimal operations.
App Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
Best app on earth! no words because it’s too good
Thomas R
iOS user
Just amazing. Let's me revise 10x better, this app is a quick 10/10. I highly recommend it to anyone. I can watch and search for notes. I can save them in the subject folder. I can revise it any time when I come back. If you haven't tried this app, you're really missing out.
Basil
Android user
This app has made me feel so much more confident in my exam prep, not only through boosting my own self confidence through the features that allow you to connect with others and feel less alone, but also through the way the app itself is centred around making you feel better. It is easy to navigate, fun to use, and helpful to anyone struggling in absolutely any way.
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
very reliable app to help and grow your ideas of Maths, English and other related topics in your works. please use this app if your struggling in areas, this app is key for that. wish I'd of done a review before. and it's also free so don't worry about that.
Rohan U
Android user
I know a lot of apps use fake accounts to boost their reviews but this app deserves it all. Originally I was getting 4 in my English exams and this time I got a grade 7. I didn’t even know about this app three days until the exam and it has helped A LOT. Please actually trust me and use it as I’m sure you too will see developments.
Xander S
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮
Elisha
iOS user
This apps acc the goat. I find revision so boring but this app makes it so easy to organize it all and then you can ask the freeeee ai to test yourself so good and you can easily upload your own stuff. highly recommend as someone taking mocks now
Paul T
iOS user