Grade 9 · Math · Unit 1 of 15
Number Sets
Whole, rational and irrational
What your child practises
Natural numbers, whole numbers, integers, rational and irrational numbers, how they fit inside each other, and why there are always more numbers between any two rational numbers.
Ontario Curriculum expectation: B1.2, B1.3 · subsets of the number system, density, infinity and limits
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
A student says every rational number is an integer. Which counterexample proves her wrong?
- 0
- 3
- −6
- 1/2
Show answer
1/2
Hint: 1/2 is a ratio of integers but not an integer.
Question 2
Which best describes the set of integers?
- The whole numbers and their opposites
- All fractions
- Numbers whose decimals never end
- Only the positive numbers
Show answer
The whole numbers and their opposites
Hint: Integers include 0, the positive whole numbers and the negatives of those numbers.
Question 3
Which set contains 0 but not −2?
- Rational numbers
- Integers
- Whole numbers
Show answer
Whole numbers
Hint: Whole numbers start at 0 and go up. Integers and rational numbers include negatives.
Question 4
What does it mean to say the rational numbers are dense?
- Rational numbers cannot be written as fractions
- Between any two rational numbers there is always another one
- Every rational number is a whole number
- There is a largest rational number
Show answer
Between any two rational numbers there is always another one
Hint: Dense means there are no gaps: the average of two rational numbers is another rational number between them.
Question 5
Which decimal is rational?
- 3.14159265… (never repeats or ends)
- 0.272727… (the digits 27 repeat)
- 1.41421356… (never repeats or ends)
- 0.1010010001… (the pattern never repeats)
Show answer
0.272727… (the digits 27 repeat)
Hint: A repeating decimal can be written as a fraction.
Question 6
Which of these is a rational number?
- π
- √2
- √5
- 0.75
Show answer
0.75
Hint: 0.75 = 3/4, a ratio of integers.