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Transcript
Properties of Real Numbers Objective: (1) To graph and order real numbers (2) To identify and use properties of real numbers Subsets of Real Numbers Rational Numbers 3 ,8,0.14,0. 3 5 Integers ... -3, -2, -1, 0, 1, 2, 3… Whole Numbers 0, 1, 2, 3, … Natural/Counting Numbers 1, 2, 3, … Irrational Numbers 2, , e Definitions Opposite (additive inverse): The opposite of any number a is –a. The sum of opposites is 0. Reciprocal (multiplicative inverse): The reciprocal of any non-zero number a is 1/a. The product of reciprocals is 1. Absolute Value: The absolute value of a number is the number’s distance from zero on the number line. Example #1: Determining Number Sets Which set of numbers best describes the values for each variable? The cost C of admission for p people. C is rational, p is a whole number A company’s profit (or loss) P in dollars for each quarter q. P is rational, q is a whole number The ratio of a circle’s circumference C with diameter d C is irrational, d is rational Example #2: Graphing Numbers on a Number Line Graph the numbers -3/2, 1.7, 5 -4 -2 0 2 4 Example #3: Finding Inverses Find the opposite and the reciprocal of each number. 3 a. -3.2 b. 5 3 3.2 opposite 5 3 .2 reciprocal 5 3 .2 1 3 .2 1 1 3. 2 1 10 5 3.2 32 16 3 Example #4: Finding Absolute Value Find each absolute value: a. 12 12 b. -5.6 5.6 c. 5 – 8 -3 3