Class 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.
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.Write 3/8 as a decimal.
2.Is every whole number also a rational number?
- a) Yes — a whole number n can be written as n/1
- b) Only when it is positive
- c) No — whole numbers are a separate kind of number
- d) Only when it is even
3.Every square root of a perfect square is rational. Tap where -√4 sits.
Mark the line with an X.
4.Match each number to the smallest family it belongs to.
- 12
- -7
- 5/6
- √11
- Whole number
- Integer, but not a whole number
- Rational, but not an integer
- Irrational
5.Put these numbers in order, smallest first.
- 1.5
- √2
- 2
- √3
6.Sort each number by whether it is rational or irrational.
Groups: Rational · Irrational
- √25
- π
- √7
- 0.25
- 3/7
- √2
7.Which of these is irrational?
- a) √36
- b) √11
- c) 0.6
- d) 2/9
8.The decimal expansion of a rational number is always...
- a) terminating, always
- b) terminating or recurring
- c) recurring, always
- d) never-ending and never repeating
Answer key — Class 9 Maths — Number systems
- 1.
- 0.375
- .375
- 2. a) Yes — a whole number n can be written as n/1
- 3. -2
- 4. 12 → Whole number; -7 → Integer, but not a whole number; 5/6 → Rational, but not an integer; √11 → Irrational
- 5. 1. √2 2. 1.5 3. √3 4. 2
- 6. 3/7 → Rational; √2 → Irrational; 0.25 → Rational; π → Irrational; √25 → Rational; √7 → Irrational
- 7. b) √11
- 8. b) terminating or recurring