Repeating Decimals to Fractions & Mixed Numbers Worksheet Bundle

Three worksheets on recurring decimals. The exercises require converting recurring decimals to fractions, comparing numbers and examining whether a given fraction can be converted to a decimal number with finitely many decimals. Detailed solutions are provided.

Master converting recurring decimals to fractions and mixed numbers with this no-prep KS3/KS4 maths bundle. Includes size comparisons and full worked keys!

Save time and money with this comprehensive, ready-to-print Recurring Decimals and Fractions maths bundle!
This high-quality printable pack brings together three complete resources designed to eliminate confusion around notation and build total procedural fluency across rational numbers. Moving sequentially from basic single-digit recurring decimals to multi-digit algebra proofs, size comparisons, and denominator factorisation, this pack provides weeks of independent practice, homework tasks, or revision material. It is an exceptional match for Key Stage 3 (KS3) and Key Stage 4 (KS4) Higher Tier GCSE preparation or IGCSE Mathematics courses.

What resources are included in this bundle?
• Resource 1: Converting Recurring Decimals to Fractions & Comparisons
o Focuses on converting recurring notations into simplified fractions, progressing from basic single-digit repetitions to complex mixed variants (including numbers like 0.6 dot, 2.7 dot, 0.15 with a dot on the 5, and 5.134 with dots on the 3 and 4).
o Features size comparison and ordering tasks where pupils evaluate values side-by-side using inequality symbols and arrange strings of decimals in ascending order.
• Resource 2: Converting Recurring Decimals to Mixed Numbers
o Advanced practice shifting from pure fractions to mixed numbers (including numbers like 2.145 with dots on the 4 and 5, and 12.136 with dots on the 3 and 6).
o Strengthens formal algebraic fraction proofs using simultaneous 10x, 100x, and 1000x subtraction tracking methods.
• Resource 3: Terminating vs. Recurring Fractional Proofs
o Conceptual tasks testing prime factorisation rules to determine if a fraction expands into a finite decimal without performing long division.
o Pupils learn to reduce fractions to lowest terms and inspect denominators for prime factors other than 2 or 5 (like checking for 3 or 7) to prove if a fraction terminates or recurs endlessly.

Why Teachers Love This Bundle:
• Excellent Value: Purchasing this all-in-one pack gives you a built-in discount compared to buying each resource individually.
• Zero Prep Required: Simply download, print out the PDFs, and hand them directly to your classes—perfect for main lessons, homework tasks, or emergency cover work.
• Progressive Rigour: Within every file, questions naturally scale from fundamental conversion mechanics to challenging exam-style extension questions.
• Fully Worked Solutions: Every single worksheet includes a thorough teacher memorandum guide showing the exact algebraic processes, prime factor steps, and final fraction simplifications for effortless marking.

Curriculum & Exam Board Alignment:
• UK National Curriculum: Key Stage 3 (KS3) and Key Stage 4 (KS4) Higher Tier Mathematics – Working with fractions, decimals, and percentages, including changing recurring decimals to fractions.
• Exam Boards: Highly relevant for Edexcel, AQA, and OCR GCSE Maths (Higher Tier) modules.