Number Sets

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

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