This deep dive covers Converting Recurring Decimal → Fraction 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 3 of 6 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.
Converting Recurring Decimal → Fraction
1
Let x = the recurring decimal
2
Multiply by 10, 100, 1000... to shift the decimal point so repeating part lines up
3
Subtract to eliminate the recurring part
4
Solve for x and simplify
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 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
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...