Classifying Real Numbers.notebook September 02, 2014 Classifying Real Numbers 1 Classifying Real Numbers.notebook September 02, 2014 Real abbreviation Numbers (R) The set of all natural, whole, integers, 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 (counting 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 fractions, including integers and improper fractions. The set of all real numbers that can be written as a ratio of two integers (fraction) 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 number 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 line. For example, ­7 is an integer, so it is also a rational and a real number. The square root of 2 is an irrational number, 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. 14 Classifying Real Numbers.notebook September 02, 2014 15.