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9th grade · Math · Unit 6 of 18

Number Sets

Whole, rational and irrational

What your child practices

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.

California Content Standards learning standard: N-RN.3 · comparing rational and irrational numbers

How we explain it

Children can open this short lesson before they practice.

  1. Natural numbers count: 1, 2, 3. Integers add 0 and negatives.
  2. Rational numbers can be written as fractions. Irrational numbers cannot.
  3. Between any two rational numbers there is always another one.

Example: Is 0.25 rational or irrational? 0.25 = 25/100 = 1/4. It is a fraction of whole numbers. Answer: Rational

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

  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

  3. Question 3

    Which set contains 0 but not −2?

    • Rational numbers
    • Integers
    • Whole numbers

  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

  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)

  6. Question 6

    Which of these is a rational number?

    • π
    • √2
    • √5
    • 0.75

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