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Rational vs. Irrational Numbers

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Rational vs. Irrational Numbers

Help a team of number detectives sort clues from a maths escape room. A rational number can be written as a fraction of integers; its decimal terminates or eventually repeats. An irrational number cannot be written as such a fraction; its decimal goes on without repeating. Show your reasoning where asked.

Sort the number clues

Classify each number. Remember: a square root of a perfect square is rational, but a square root of a non-perfect square is irrational.

1.The first keypad code is 0.75. Is 0.75 rational or irrational?
  • Rational
  • Irrational
2.A clue card shows √9. Is √9 rational or irrational?
  • Rational
  • Irrational
3.The alarm code is √2. Is √2 rational or irrational? Give one reason.
4.The final clue is π. Is π rational or irrational?
  • Rational
  • Irrational

Place and explain

Use the number line for the next clue. It runs from 0 to 3 in steps of 0.5.

5.Place √2 on the number line. Use the estimate √2 ≈ 1.414 to show where it belongs between the labelled marks.
00.511.522.53
6.Which number is closest to √2 ≈ 1.414?
  • 1.3
  • 1.41
  • 1.5
7.Select every rational number in this set: 22/7, π, √16, 0.121212… (the digits 12 repeat).

Solve the escape-room challenge

A square has sides that are each 1 unit long. Its diagonal is labelled d.

8.Use Pythagoras’ theorem to find the exact length of the square’s diagonal d. Then classify d as rational or irrational.
9.A teammate says, “22/7 is irrational because it is often used as an estimate for π.” Is the teammate correct? Explain the difference between 22/7 and π.
10.Exit ticket: classify −3/4, √8 and 0.333… (the digit 3 repeats). Give a brief reason for each.

2 printable pages

  • Rational vs. Irrational Numbers, page 1 of 2: Sort the number clues, Place and explain

    Page 1

  • Rational vs. Irrational Numbers, page 2 of 2: Solve the escape-room challenge

    Page 2

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