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Grade 8 · The Number System · 8.NS.A.1

Rational and Irrational Numbers Worksheets

Free, printable, and ready to teach: a practice worksheet, homework, an exit ticket, and an answer key with step-by-step solutions — plus lesson slides you can edit. No sign-up needed.

First page of the rational and irrational numbers practice worksheet

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PDFs print on US Letter paper. Free for classroom and home use.

Step-by-step math videos on the Math With Mr DJ YouTube channel →

Key idea

Rational: terminates (0.125) or repeats (0.333…). Irrational: neither. ‘Forever’ is not the test — ₁⁄₃ goes on forever and is rational.

Sample problems

Write 0.6 and −0.125 as fractions.
Which of these are rational? 7, −₃⁄₄, 0.5, 0.121212…
Is √36 rational or irrational? What about √37?
Explain why ‘the decimal goes on forever’ does not make a number irrational. Give an example.

Common mistakes to watch for

Answered irrational because it is written as a decimal rather than a fraction. Notation is not a property of the number.
Agreed with her. This is THE misconception in the topic: ‘goes on forever’ is being used as the definition of irrational, and it makes every repeating decimal wrong.
Put √16 with the irrationals, over-generalising from the radical sign. Or put 0.181818… with the irrationals, using the forever-test again.

The answer key explains each one, so you can tell what a wrong answer means.

How to use this set

Teach with the slides (about 15 minutes), or watch the video together.
Practice with the worksheet. Questions climb from fluency to application to reasoning.
Check understanding with the exit ticket, and send the homework home.
Mark with the answer key — each answer shows the steps and the most likely mistake.

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