About this worksheet

This free Year 8 rational and irrational numbers worksheet is written for the Western Australian curriculum and mapped to SCSA content description WA8MNAUN1. It targets one skill so students can practise until it sticks: by the end, students can say “I can define and identify rational and irrational numbers and use correct notation for terminating, recurring and rounded decimals.”

What’s inside

• Key idea box – a short explanation with worked examples to read before starting.
• A · Fluency (16 questions) – quick practice to build accuracy.
• B · Core (10 questions) – worded problems set in everyday Australian contexts.
• C · Reasoning (4 questions) – explain, justify and spot the error.
• D · Challenge (4 questions) – harder multi-step and problem-solving questions for students ready to stretch.
• Separate marking key – every answer with working, plus mark allocations and marking criteria for reasoning questions.

Skills covered

• Classifying numbers as rational or irrational
• Writing integers, terminating and recurring decimals as fractions
• Estimating square roots between consecutive whole numbers

How to use this worksheet

Start with the Key idea box, then complete Section A (use a calculator only where a question says so). Most students should attempt Sections B and C; Section D suits students aiming for the top of the class or preparing for accelerated or extension maths. The worksheet is marked out of 58, and the score box on the last page helps students see which section needs more practice.

Common mistakes to watch for

• Thinking all square roots are irrational
• Believing 22/7 is exactly equal to π
• Treating a rounded calculator display as a terminating decimal
• Forgetting that integers are rational

Where this fits in the WA Year 8 sequence

Rational and Irrational Numbers sits in the Understanding number sub-strand of Number and algebra. It is one of a set of short, single-skill EduLift worksheets that split each Year 8 content description into sub-skills. Use the previous and next links to work through the sequence in order.

Common errors we see in tutoring

• Thinking all square roots are irrational
• Believing 22/7 is exactly equal to π
• Treating a rounded calculator display as a terminating decimal
• Forgetting that integers are rational