Virginia SOL Math / Grade 8 / Number & Number Sense

8.NS.2

Subsets of the Real Numbers

What you'll learn

  • Describe the subsets of the real number system
  • Classify a number as natural, whole, integer, rational, or irrational
  • Give examples that belong to more than one subset

Words to know

Natural numbers —
the counting numbers 1, 2, 3, and so on
Whole numbers —
the natural numbers together with 0
Integers —
whole numbers and their opposites, like -3, 0, 5
Rational number —
any number that can be written as a fraction of two integers
Irrational number —
a real number that cannot be written as such a fraction

Why it matters Knowing which set a number belongs to helps us predict how it behaves and choose the right tools when we compute or estimate.

Worked examples

Model ItI do

Name every subset that -6 belongs to.

The number -6 is an integer because it is a whole number and its opposite. It is also rational because it can be written as -6/1. It is not a natural or whole number because those do not include negatives.

Try It TogetherWe do

Classify 0.75 and the square root of 3.

The number 0.75 equals 3/4, a ratio of integers, so it is rational. The square root of 3 is about 1.732... and never ends or repeats, so it is irrational.

Now YouYou do

Classify the number 12 using every subset it belongs to.

List each subset from natural down to real that includes 12. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Is the number 7 a natural number?

  2. 2.Classify -2: is it a whole number?

  3. 3.Is 1/2 rational or irrational?

On Level

The core Quick Check from the book.

  1. 1.Is -8 a whole number? Explain in one word.

  2. 2.Classify 5/6 as rational or irrational.

  3. 3.Classify the square root of 16.

  4. 4.Name one number that is an integer but not a natural number.

  5. 5.Is 0 a natural number?

Challenge

Stretch your thinking.

  1. 1.Name every subset of the real numbers that the number 9 belongs to.

  2. 2.The square root of 36 is claimed to be irrational. Is that true? Explain.

  3. 3.Give one number that is rational but NOT an integer, and one that is irrational.