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1.3 Exploring Real Numbers Textbook pg 17 Terminology • • • • Natural Numbers: {1, 2, 3, 4, 5, 6,…} Whole Numbers: {0, 1, 2, 3, 4, 5,…} Integers: {…,-3, -2, -1, 0, 1, 2, 3, …} A Rational Number is any number that a can be written in the form b where b≠0 and a and b are integers, or as a terminating or repeating decimal. • An Irrational Number is any number that a cannot be written in the form b where b≠0 and a and b are integers, or as a terminating or repeating decimal. • Together, rational and irrational numbers for the set of Real Numbers. Real Numbers Rational Numbers Integers Whole Numbers Irrational Numbers Any example that proves a statement false is a Counterexample. – All odd numbers end in 3 – Counter example: 25 To find the Opposite of a number, change its sign. • The opposite of positive is negative – The opposite of 3 is -3 • The opposite of negative is positive – The opposite of -10 is 10 Absolute Value • A number’s absolute value is its distance away from Zero on the number line • Absolute Value is ALWAYS positive because you cannot have negative distance Find Each Absolute Value 1) 4 = 4 2 ) 21 = 21 3) 1 2 =½ 4) -6 4 = 2 5 ) 12 4 = 48 An Inequality is a mathematical sentence that compares the value of two expressions using an inequality symbol such as: • • ‹ › •≤ •≥ •≠ Less Than Greater Than Less Than OR Equal To Greater Than OR Equal To Not Equal To Comparing Using Inequalities 2 1) 3 2) 2 3 1 › ‹ = 3) 19 4) 3 . 11 6 1 6 - 19 ‹ 7 . 83 Assignment # 3 • Beginning on textbook page 20 • Problems 42-63 all, 68-72 all, 79-85 all, 87-95 odd • Write all problems except for the word problems. Show all of your work. • Do not pack up until instructed to do so by the teacher.