Maths Resources GCSE Worksheets


Rational And Irrational Numbers Worksheet

Rational And Irrational Numbers Worksheet

Help your students prepare for their Maths GCSE with this free rational and irrational numbers worksheet of 44 questions and answers

  • Section 1 of the rational and irrational numbers worksheet contains 36 skills-based rational and irrational numbers questions, in 3 groups to support differentiation
  • Section 2 contains 4 applied rational and irrational numbers questions with a mix of worded problems and deeper problem solving questions
  • Section 3 contains 4 foundation and higher level GCSE exam style rational and irrational numbers questions 
  • Answers and a mark scheme for all rational and irrational numbers questions are provided
  • Questions follow variation theory with plenty of opportunities for students to work independently at their own level
  • All questions and math worksheets are created by fully qualified expert secondary maths teachers
  • Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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Rational and irrational numbers at a glance


Within the real number system, a rational number is any number that can be expressed in the form “p over 1” where p and q are integers. Whole numbers, terminating decimals and recurring decimals (repeating decimals) are all rational numbers. 


Irrational numbers are numbers which cannot be written in the form “p over q”. When written as decimals, irrational numbers go on forever without repeating. Examples of irrational numbers include the square root of any number that is not a perfect square and pi.


Looking forward, students can then progress to additional number worksheets, for example a fractions worksheet or a rounding worksheet.




For more teaching and learning support on Number our GCSE maths lessons provide step by step support for all GCSE maths concepts.

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GCSE Maths Worksheets

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Lessons are selected to provide support where each student needs it most, and specially-trained GCSE maths tutors adapt the pitch and pace of each lesson. This ensures a personalised revision programme that raises grades and boosts confidence.

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