Convert 0.7ฬ 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 โ x = 7.777... โ 0.777...
9x = 7
Step 4 Solve for x
x = 7/9
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 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Recurring Decimals
Which of these fractions gives a recurring decimal when you divide?
Explain why 1/6 gives a recurring decimal. You must refer to prime factors in your answer.
Quick recall flashcards
What does dot notation mean in recurring decimals?
A dot above a single digit: that digit repeats. 0.3ฬ = 0.333...
Dots above two digits: the entire block between them repeats. 0.1ั8ั = 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