NumberStudy Notes

Worked Example 1: Simple Recurring

Part of Recurring DecimalsGCSE Mathematics

This study notes covers Worked Example 1: Simple Recurring within Recurring Decimals for GCSE Mathematics. Revise Recurring Decimals in Number for GCSE Mathematics with 14 exam-style questions and 11 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 4 of 5 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 5

Practice

14 questions

Recall

11 flashcards

Worked Example 1: Simple Recurring

Convert 0.7̇ to a fraction

Step 1 Let x = 0.777...

x = 0.777777...

Step 2 Multiply by 10

10x = 7.777777...

Step 3 Subtract x from 10x

10x − x = 7.777... − 0.777...

9x = 7

Step 4 Solve for x

x = 7/9

Keep building this topic

Read this section alongside the surrounding pages in Recurring Decimals. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Recurring Decimals

Which of these fractions gives a recurring decimal when you divide?

  • A. 1/3
  • B. 1/4
  • C. 3/5
  • D. 7/8
1 markfoundation

Explain why 1/6 gives a recurring decimal. You must refer to prime factors in your answer.

3 markschallenge

Quick Recall Flashcards

What does dot notation mean in recurring decimals?
A dot above a single digit: that digit repeats. 0.3̇ = 0.333... Dots above two digits: the entire block between them repeats. 0.1ї8ї = 0.181818...
What is a recurring decimal?
A decimal where one or more digits repeat infinitely in a regular pattern. Examples: 0.333... = 1/3, 0.090909... = 1/11

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