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Year 9 Maths — Number systems

Tell a rational number from an irrational one, and place any real number on the number line.

Name: ________________________

Before you start

Every tick on this line is a rational number. Move along it and watch where √2 (about 1.41), √3 (about 1.73) and π (about 3.14) would have to squeeze in.

0.00.51.01.52.02.53.03.54.0

No tick will ever land exactly on √2, however finely you chop the line up. That is what irrational means — not that the number is missing, but that no fraction can name it.

  1. 1.√25 turns out to be rational. Which whole number is it equal to?

  2. 2.Write the recurring decimal 0.777… as a fraction in simplest form.

  3. 3.Write 3/8 as a decimal.

  4. 4.Every square root of a perfect square is rational. Tap where -√4 sits.

    Mark the line with an X.

    -5-4-3-2-1012345

  5. 5.√2 is 1.414 to three decimal places. Tap the tick it is nearest to.

    Mark the line with an X.

    1.01.52.0

  6. 6.Which of these is irrational?

    • a) 0.6
    • b) √36
    • c) 2/9
    • d) √11

  7. 7.Is every whole number also a rational number?

    • a) Only when it is positive
    • b) Only when it is even
    • c) No — whole numbers are a separate kind of number
    • d) Yes — a whole number n can be written as n/1

  8. 8.Match each number to the smallest family it belongs to.

    • 12
    • -7
    • 5/6
    • √11
    • Rational, but not an integer
    • Irrational
    • Whole number
    • Integer, but not a whole number

Answer key — Year 9 Maths — Number systems

  1. 1. 5
  2. 2. 7/9
  3. 3.
    • 0.375
    • .375
  4. 4. -2
  5. 5. 1.4
  6. 6. d) √11
  7. 7. d) Yes — a whole number n can be written as n/1
  8. 8. 12 → Whole number; -7 → Integer, but not a whole number; 5/6 → Rational, but not an integer; √11 → Irrational