Classifying Real .notebook September 02, 2014

Classifying Real Numbers

1 Classifying Real Numbers.notebook September 02, 2014

Real abbreviation Numbers (R)

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

2 Classifying Real Numbers.notebook September 02, 2014

Whole abbreviation Numbers (W)

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

• starts at 0 • includes all the natural ( numbers)

3 Classifying Real Numbers.notebook September 02, 2014

Natural abbreviation Numbers (N)

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

• starts at 1 • includes all the numbers used in counting

4 Classifying Real Numbers.notebook September 02, 2014

abbreviation Integers (Z)

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

All positive and negative whole numbers, including zero.

5 Classifying Real Numbers.notebook September 02, 2014

Rational abbreviation Numbers (Q)

All positives and negative , including integers and improper fractions. The set of all real numbers that can be written as a of two integers () with 3 1 a nonzero denominator. /4, ‐ /5, 3.72, 7

6 Classifying Real Numbers.notebook September 02, 2014

Irrational abbreviation Numbers (I)

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

Examples: ­√2, √7, √19, π, ... √4 = 2 (rational)

7 Classifying Real Numbers.notebook September 02, 2014

Number Systems Concept Map 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.

Real Numbers

Rational Irrational Integers Whole Natural

8 Classifying Real Numbers.notebook September 02, 2014

Q ­ Rational Numbers Drag the numbers into the correct category. Remember that each may go into more Z ­ Integers than one category.

12 ­5 7/9 W ­ Whole Numbers 2.2 √10

N ­ Natural Numbers 1.33 ­3/4 √73 36 √15 I ­ Irrational Numbers ­√2 0 1.25 ­1

9 Classifying Real Numbers.notebook September 02, 2014

­3/4 Q ­ Rational Numbers Drag the numbers into the 0 correct category. 12 7/9 2.2 1.33 ­5 ­1 Remember that each number may go into more Z ­ Integers 12 than one category. ­5 36 0 ­1 12 ­5 7/9 W ­ Whole Numbers 0 12 36 2.2 √10

N ­ Natural Numbers 1.33 ­3/4 √73 12 36 36 √15 I ­ Irrational Numbers ­√2 0 1.25 √10 √15 ­√2 ­1

10 Classifying Real Numbers.notebook 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/

11 Classifying Real Numbers.notebook September 02, 2014

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

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

12 Classifying Real Numbers.notebook September 02, 2014

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

13 Classifying Real Numbers.notebook 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.

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