Classifying Real Numbers.notebook

1

September 02, 2014

Classifying Real Numbers

Classifying Real Numbers.notebook

2

September 02, 2014

Real Numbers

The set of all natural, whole, integers, rational and irrational numbers, excluding imaginary numbers.

(R)abbreviation

Simon

Classifying Real Numbers.notebook

3

September 02, 2014

Whole Numbers

The numbers 0, 1, 2, 3, 4, ...

• starts at 0

• includes all the natural (counting numbers)

(W)abbreviation

Classifying Real Numbers.notebook

4

September 02, 2014

Natural Numbers

The numbers 1, 2, 3, 4, ...

• starts at 1

• includes all the numbers used in counting

(N)abbreviation

Classifying Real Numbers.notebook

5

September 02, 2014

Integers

The numbers

..., ­3, ­2, ­1, 0, 1, 2, 3, ...

All positive and negative whole numbers, including zero.

(Z)abbreviation

Classifying Real Numbers.notebook

6

September 02, 2014

Rational NumberssAll positive and negative

fractions, including integers and improper fractions.

(Q)abbreviation

The set of all real numbers that can be written as a ratio of two integers (fraction) with a nonzero denominator. 3/4, ‐1/5, 3.72, 7

Classifying Real Numbers.notebook

7

September 02, 2014

Irrational Numbers

Real numbers that are not rational.

Real numbers that cannot be written as a ratio of integers.

Examples: ­√2, √7, √19, π, ...

(I)abbreviation

√4 = 2 (rational)

Classifying Real Numbers.notebook

8

September 02, 2014

Number Systems Concept Map

Real Numbers

Rational IrrationalIntegersWhole

Natural

All of the natural numbers are whole numbers. All of the whole numbers are integers. All of the integers are rational numbers. All of the rational and irrational numbers are real numbers.

Classifying Real Numbers.notebook

9

September 02, 2014

Q ­ Rational Numbers

Z ­ Integers

W ­ Whole Numbers

N ­ Natural Numbers

I ­ Irrational Numbers

Drag the numbers into the correct category.

Remember that each number may go into more than one category.

12 ­5

2.2 √10

√73

√15­√2

36

7/9

1.33

0

­3/4

1.25­1

Classifying Real Numbers.notebook

10

September 02, 2014

Q ­ Rational Numbers

Z ­ Integers

W ­ Whole Numbers

N ­ Natural Numbers

I ­ Irrational Numbers

Drag the numbers into the correct category.

Remember that each number may go into more than one category.

12 ­5

2.2 √10

√73

√15­√2

36

7/9

1.33

0

­3/4

1.25­1

12 ­5 7/9 2.2

√10

1.33­3/4

√15 ­√2

0­1

12­5 36 0 ­1

0 12 36

12 36

Classifying Real Numbers.notebook

11

September 02, 2014

You tube video review of number sets

http://youtu.be/oEkkXE82MN0

Interactive game using number sets

http://www.softschools.com/math/classifying_numbers/real_rational_integer_whole_natural_irrational_number_table/

Classifying Real Numbers.notebook

12

September 02, 2014

Taking into account the irrational numbers and the real numbers, ourclassification might look like this: 

Figure %: Classification of Numbers If a number falls into a category, it also falls into all the categories belowthat category to which it is connected by a line. For example, ­7 is aninteger, so it is also a rational and a real number. The square root of 2is an irrational number, so it is also a real number.

Classifying Real Numbers.notebook

13

September 02, 2014

The chart below will help you with the classification of numbers a lot. It will makes things crystal clear. 

Classifying Real Numbers.notebook

14

September 02, 2014

Keep your notes and complete the "Sets of Real Numbers" paper for homework.  You may need to look at your notes to label the number with the correct set.  Remember, many numbers are part of more than one number set.

Classifying Real Numbers.notebook

15

September 02, 2014