Number set / Definition / Examples / Non-Examples
Natural numbers
Whole numbers
Integers
Rational numbers
Irrational numbers

The set of rational numbers and the set of irrational numbers together make up the set of real numbers. The Venn diagram below shows the relationship among the real numbers.

Real Numbers

Identify all of the subsets of real number system to which each number belongs:

1) 15 2) -28 3) 0.3

7

4) -81 5) 67 6)

7) 0.10110111…. 8) 0.235235 9) -

Name ______Block ______

Name all of the sets of numbers to which each real number belongs. Use natural numbers, whole numbers, integers, rational numbers, and irrational numbers.

1) 0.212121… 2) -41 3) 1 4) -42

4 5

5) 0.090090009… 6) 2.31 7) 45 8) 36

9

Determine whether each statement is sometimes, always, or never true.

13) A decimal number is an irrational number. ______

14) An integer is a whole number. ______

15) A natural number is an integer. ______

16) An integer is a natural number. ______

Choose the letter which best answers the question.

17) Which of the following is a whole number?

A) 3.6 B) 16 C) 8 D) Both B and C

18) Which category does 81 not belong to?

A) Irrational #’s B) Integers C) Natural #’s D) Whole numbers

______

Give an example and a non-example for each of the following subsets:

Example / Non-example / Example / Non-example
Integer / Rational Number
Whole Number / Irrational Number

Name ______Real Number System Practice

I. Classify Numbers - Complete the chart. Place an “X” in the box for each correct classification.

Example / Natural / Whole / Integer / Rational / Irrational / Real
0
4
-7
0.121212…
0.010110111…

II. Describe each subset of the real numbers. Give an example and a non-example.

Subset / Description / Example / Non-Example
Whole Numbers
Irrational Numbers
Natural Numbers
Integers
Rational Numbers

IV. True or False. Determine if the following statements are true or false. Then, explain your answer.

______1) The number 0 is a counting number. Explain your answer. ______

______2) The number is rational. Explain your answer. ______

______3) The number 0.33333… is irrational. Explain your answer. ______

______4) The number -2.5 is an integer. Explain your answer. ______

V. Determine whether each statement is sometimes, always, or never true.

1) A rational number is an irrational number ______2) A fraction is an integer. ______

3) A negative number is an integer. ______4) A counting number is a whole number. ______

0 / 0.7 / 0.121212…
–3 / / –0.9 / π
–4.267 / – / 14.8 / 0.010110111…