Mrs Volynskaya Real Numbers The Set of Natural

Mrs. Volynskaya Real Numbers

• • The Set of Natural Numbers: {1, 2, 3, …} The Set of Whole Numbers: {0, 1, 2, …} The Set of Integers {… -3, -2, -1, 0, 1, 2…} Rational numbers can be written as fractions or as decimals that either terminate or repeat: 2/7, 0. 354, 3. 555. . . , 4/5, 9. 078302 • Irrational numbers can only be written as decimals that do not terminate or repeat. If a whole number is not a perfect square, then its square root is an irrational number. √ 2, √ 3, √ 5 are Irrational • How about √ 1, √ 4 , √ 9, √ 16 ? ? ?

WORLD OF REAL NUMBERS

EXAMPLE • Classify all the following numbers as natural, whole, integer, rational, or irrational. List all that apply. a. 117 b. 0 c. -12. 64039… d. -½ e. 6. 36 f. 1/9 g. -3

EXAMPLE 77 is a Natural number, a Whole number, an Integer, and a Rational number. 9/10 is a rational number. (- 5) is an integer, and a rational number. 17. 5407… is an irrational number. -3 is an integer and a rational number. 5. 39 is a rational number. – is an irrational number. 1/7 is a rational number.

Set Notation Natural numbers Whole Numbers Integers A collection of objects. { } Counting numbers {1, 2, 3, …} Natural numbers and 0. {0, 1, 2, 3, …} Positive and negative natural numbers and zero. {… -2, -1, 0, 1, 2, 3, …} A real number that can be expressed as a ratio of integers (fraction) Any real number that is not rational. Rational Number Irrational Number Real Numbers All numbers associated with the number line.

To which set(s) of numbers does 6 belong? a) Natural Numbers b) Whole numbers c) Integers d) Rational numbers e) Irrational numbers f) Real numbers Slide 1 - 10 Copyright © 2011 Pearson Education, Inc.

To which set of numbers does 6 belong? a) Natural Numbers b) Whole numbers

Definitions Variable A symbol that can vary in value. Constant A symbol that does not vary in value. A mathematical relationship that does not contain an equal sign Expression Equation A mathematical relationship that contains an equal sign. Inequality A mathematical relationship that contains an inequality symbol ( , <, >, , or ). Absolute Value A given number’s distance from 0 on a number line. Notation = | |.