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Question 18 - OCR GCSE Higher 2020 Past Paper 6 - Numbers,Decimals,Recurring Decimals,Fractions,Algebra,Algebraic Equations,Linear Equations Questions By Topic

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Question 26 - AQA GCSE Higher 2020 Past Paper 3 - Algebra, Algebraic Proof, Numbers, Recurring Decimals, Decimals Questions By Topic

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Question 14 - OCR GCSE Higher 2018 Past Paper 6 - Numbers, Decimals Questions By Topic

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Question 31 - AQA GCSE Higher Specimen Paper 1 - Numbers, Decimals Questions By Topic

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Question 15 - Edexcel GCSE Higher 2017 Maths Past Paper 1 - Numbers Decimals Decimals to Fractions Recurring Decimals Algebra, Linear Equations Questions By Topic

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Recurring Decimals - GCSE Mathematics - Revision and Examples

1. Recurring Decimals

Recurring Decimals are those numbers that keep on repeating the same value after a decimal point. These numbers are also called Repeating Decimals. 

For example, 1/3 = 0. = 0.3333…

Fractions in which the denominator has prime factors of only 2 or 5 will terminate (not repeat).

1.1 How to convert recurring decimals to fractions?

Converting recurring decimals to fractions is representing a recurring decimal as a fraction without changing its value.

For example,

0.24¯ = 0.24242424…

0.123¯ = 0.123123123… are all examples of recurring decimals.

Let's check the following steps involved in converting Repeating Decimals to fractions.

  1. Let 'x' be the Repeating Decimal number that we want to convert into a rational number. 
  2. Observe the Repeating Decimal to identify the repeating digits. 
  3. Carefully place the repeating digits to the left of the decimal point. 
  4. Place the repeating digits to the right of the decimal point. 
  5. Now deduct the left sides of the two equations. Then, apply the subtraction on the right side of the two equations. As we subtract, always ensure the differences between both sides should be positive.

Example: Convert 0.7 (one recurring digit) into a fraction. 

Solution:

Recurring Decimals Example Solution 01

Example: Prove algebraically 3.47777… = 313/90

Solution: 

Recurring Decimals Example Solution 02

Example: Prove algebraically that 0.73333… can be written as 11/15.

Solution: 

Recurring Decimals Example Solution 03

Quiz Questions
01. GCSE Recurring Decimals

GCSE Topics

  • Statistical Measures (5)
  • Numbers (1,084)
  • Data Visualisation (4)
  • Algebra (1,176)
  • Ratio, Proportion and Rates of Change (443)
  • Geometry and Measures (809)
  • Statistics (274)
  • Probability (258)
  • Frequently Asked Questions
    What are the main topics in GCSE Maths?

    The main topics in GCSE Maths are:

    • Numbers
    • Algebra 
    • Ratio, Proportion and Rates of Change 
    • Geometry and Measures
    • Statistics 
    • Probability 
    • Statistical Measures 
    • Data Visualisation 

    With regular practice of GCSE Maths topic-wise questions and GCSE Maths past pacers, you can easily score high marks.

    Is GCSE Maths hard?

    Although many people think of GCSE maths as a difficult subject, with the correct training and preparation,you can master it in time. You can practice GCSE Maths  topic-wise questions daily to improve speed, accuracy, and time and to score high marks in the GCSE Maths exam.

    What is a good grade on GCSE Maths Exam?

    A grade of 4 or 5 would be considered "good" because the government has established a 4 as the passing grade; a grade of 5 is seen as a strong pass. Therefore, anything that exceeds this level would be considered good. You can practice GCSE Maths topic-wise questions to score good grades in the GCSE Maths exam.

    How can I get full marks in GCSE Maths?

    You can get a high score in GCSE Maths through meticulous practice of GCSE Maths topic-wise questions and GCSE Maths past papers.

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