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Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

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Page 1: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classifying Numbers

Whole NumbersIntegers

Rational NumbersIrrational Numbers

Real Numbers

Page 2: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Whole numbers consist of any positive number which does not have fractional parts.

This set also includes zero.

0, 1, 2, 3, 4, 5, 6, 7, …

Fractions Mixed Numbers

Negative Numbers

Page 3: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Integers are whole numbers both positive and negative. This set also includes zero.

…, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …

Fractions Mixed Numbers

Page 4: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Notice that the set of whole numbers is included in the set of integers.

WholeNumbers

Integers

Page 5: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Rational numbers include all integers as well as terminating & repeating decimals, fractions, and mixed number.

…, -3,-2.75, -2, -1, 0, ½, .7, 1, 2, 3, 3.5 …

Nonterminating, nonrepeating decimals

Page 6: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

What isn’t a rational number

Page 7: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

These numbers are irrational. They are nonrepeating, nonterminating decimals.

= 3.141592653…

2 = 1.414213562…

5 = 2.23606797…

Note: These are square roots of non-perfect squares.

Page 8: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Rational numbers include both integers and whole numbers.

WholeNumbers

Integers

Rationals

Page 9: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as whole, integer, or rational. You may give multiple names to each number.

1) .7

2) -4

3) 2.75

4) .3

5) 25

6) -2½

Page 10: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as whole, integer, or rational. You may give multiple names to each number.

1) .7 rational

2) -4

3) 2.75

4) .3

5) 25

6) -2½

Page 11: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as whole, integer, or rational. You may give multiple names to each number.

1) .7 rational

2) -4 integer, rational

3) 2.75

4) .3

5) 25

6) -2½

Page 12: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as whole, integer, or rational. You may give multiple names to each number.

1) .7 rational

2) -4 integer, rational

3) 2.75 rational

4) .3

5) 25

6) -2½

Page 13: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as whole, integer, or rational. You may give multiple names to each number.

1) .7 rational

2) -4 integer, rational

3) 2.75 rational

4) .3 rational

5) 25

6) -2½

Page 14: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as whole, integer, or rational. You may give multiple names to each number.

1) .7 rational

2) -4 integer, rational

3) 2.75 rational

4) .3 rational

5) 25 whole, integer, rational

6) -2½

Page 15: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as whole, integer, or rational. You may give multiple names to each number.

1) 0.7 rational

2) -4 integer, rational

3) 2.75 rational

4) 0.3 rational

5) 25 whole, integer, rational

6) -2½ rational

Page 16: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Place the following numbers in the appropriate location on the diagram:-5 2.6 ½ 6/1 0 14 -4 ¾ 4.0

WholeNumbers

Integers

Rationals

Page 17: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Place the following numbers in the appropriate location on the diagram:-5 2.6 ½ 6/1 0 14 -4 ¾ 4.0

WholeNumbers

Integers

Rationals

-5

Page 18: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Place the following numbers in the appropriate location on the diagram:-5 2.6 ½ 6/1 0 14 -4 ¾ 4.0

WholeNumbers

Integers

Rationals

-5

2.6

Page 19: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Place the following numbers in the appropriate location on the diagram:-5 2.6 ½ 6/1 0 14 -4 ¾ 4.0

WholeNumbers

Integers

Rationals

-5

2.6½

Page 20: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Place the following numbers in the appropriate location on the diagram:-5 2.6 ½ 6/1 0 14 -4 ¾ 4.0

WholeNumbers

Integers

Rationals

-5

2.6½

6/1

Page 21: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Place the following numbers in the appropriate location on the diagram:-5 2.6 ½ 6/1 0 14 -4 ¾ 4.0

WholeNumbers

Integers

Rationals

-5

2.6½

6/1 0

Page 22: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Place the following numbers in the appropriate location on the diagram:-5 2.6 ½ 6/1 0 14 -4 ¾ 4.0

WholeNumbers

Integers

Rationals

-5

2.6½

6/1 0

14

Page 23: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Place the following numbers in the appropriate location on the diagram:-5 2.6 ½ 6/1 0 14 -4 ¾ 4.0

WholeNumbers

Integers

Rationals

-5

2.6½

6/1 0

14

-4 ¾

Page 24: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Place the following numbers in the appropriate location on the diagram:-5 2.6 ½ 6/1 0 14 -4 ¾ 4.0

WholeNumbers

Integers

Rationals

-5

2.6½

6/1 0

14

-4 ¾

4.0

Page 25: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

The set of rational numbers and irrational numbers comprise the set of real numbers.

Integers

Rationals

WholeNumbers

Irrationals

Real Numbers

Page 26: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Decide whether each number is rational or irrational.

1)

2)

3) -6

4)

5) 2.4545454545…

6) 7.25

7)

8)

25

30

16

8

40

Page 27: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Decide whether each number is rational or irrational.

1) rational

2)

3) -6

4)

5) 2.4545454545…

6) 7.25

7)

8)

25

30

16

8

40

Page 28: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Decide whether each number is rational or irrational.

1) rational

2) irrational

3) -6

4)

5) 2.4545454545…

6) 7.25

7)

8)

25

30

16

8

40

Page 29: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Decide whether each number is rational or irrational.

1) rational

2) irrational

3) -6 rational

4)

5) 2.4545454545…

6) 7.25

7)

8)

25

30

16

8

40

Page 30: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Decide whether each number is rational or irrational.

1) rational

2) irrational

3) -6 rational

4) rational

5) 2.4545454545…

6) 7.25

7)

8)

25

30

16

8

40

Page 31: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Decide whether each number is rational or irrational.

1) rational

2) irrational

3) -6 rational

4) rational

5) 2.4545454545… rational

6) 7.25

7)

8)

25

30

16

8

40

Page 32: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Decide whether each number is rational or irrational.

1) rational

2) irrational

3) -6 rational

4) rational

5) 2.4545454545… rational

6) 7.25 rational

7)

8)

25

30

16

8

40

Page 33: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Decide whether each number is rational or irrational.

1) rational

2) irrational

3) -6 rational

4) rational

5) 2.4545454545… rational

6) 7.25 rational

7) irrational

8)

25

30

16

8

40

Page 34: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Decide whether each number is rational or irrational.

1) rational

2) irrational

3) -6 rational

4) rational

5) 2.4545454545… rational

6) 7.25 rational

7) irrational

8) irrational

25

30

16

8

40

Page 35: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

What isn’t a real number

Page 36: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

These “numbers” are NOT real numbers.

9

15

24

0

5

0

3 0

12

You cannot find the square root of a negative number.

You cannot divide by zero.

Page 37: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as real or not real.

1)

2)

3)

4)

5)

25

8

64

0

4

4

0

Page 38: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as real or not real.

1) Not real

2)

3)

4)

5)

25

8

64

0

4

4

0

Page 39: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as real or not real.

1) Not real

2) Real

3)

4)

5)

25

8

64

0

4

4

0

Page 40: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as real or not real.

1) Not real

2) Real

3) Real

4)

5)

25

8

64

0

4

4

0

Page 41: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as real or not real.

1) Not real

2) Real

3) Real

4) Not real

5)

25

8

64

0

4

4

0

Page 42: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Classify each number as real or not real.

1) Not real

2) Real

3) Real

4) Not real

5) Not real

25

8

64

0

4

4

0

Page 43: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Whole Numbers

0 1 2 3

Page 44: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Integers

-3 -2 -1 0 1 2 3

Page 45: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Rational Numbers

-3 -2 -1 -.75

0 1 2 3

2

14

12 3.2

Page 46: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Irrational Numbers

π5 142 2614

Page 47: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

REAL NUMBERS =

Irrational Numbers

π5 142 2614

Rational Numbers-3 -2 -1

-.750 1 2 3

2

14

12 3.2

+

Page 48: Classifying Numbers Whole Numbers Integers Rational Numbers Irrational Numbers Real Numbers

Integers

Rationals

WholeNumbers

Irrationals

Real Numbers Numbers

that are NOT real.

Give 2 examples of each kind of number.