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Numbers Foundation Concepts. 7/2/2013 Numbers 2 The Real Numbers The number line Numbers 0 1 2 3 1 2 3 4 19 12 1 2 -  2 e  3.14 = 2.718281828   2.

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Presentation on theme: "Numbers Foundation Concepts. 7/2/2013 Numbers 2 The Real Numbers The number line Numbers 0 1 2 3 1 2 3 4 19 12 1 2 -  2 e  3.14 = 2.718281828   2."— Presentation transcript:

1 Numbers Foundation Concepts

2 7/2/2013 Numbers 2 The Real Numbers The number line Numbers 0 1 2 3 1 2 3 4 19 12 1 2 -  2 e  3.14 = 2.718281828   2 - The set of real numbers is called R 22 7 = 3.14 = 459045… 28571428571... 15926535897…  3 - 2 Repeating group  5 Binary Relations

3 7/2/2013 Numbers 3 The Real Numbers Is there always a number between a and b ? Numbers a b a + b 2 Average of a and b is midway between a and b After b, what is the next real number? Question:

4 7/2/2013 Numbers 4 The Natural Numbers The Set of Counting Numbers N = { 1, 2, 3, 4, … } The Integers Positive and Negative Natural Numbers I = { … -3, -2, -1, 0, 1, 2, 3, … } Subsets of the Real Numbers … and Zero Binary Relations

5 7/2/2013 Numbers 5 Rational Numbers Solutions of linear equations a x + b = 0 for integers a, b Proper fractions and integers Subsets of the Real Numbers Q = { | a, b are integers, b ≠ 0 } a b

6 7/2/2013 Numbers 6 Irrational Numbers Not solutions of a x + b = 0 Algebraic numbers – roots of n th degree polynomials with rational coefficients Examples: x 2 – 2 = 0 x 3 – 5 = 0 Transcendental numbers Subsets of the Real Numbers { x | x  R, x  Q } x =  2 + – 3  5

7 7/2/2013 Numbers 7 Irrational Numbers Not solutions of a x + b = 0 Transcendental numbers – Examples:  = 3.1415 92653 58979 32384 62643 … e = 2.7182 81828 45904 52353 60287 … Subsets of the Real Numbers { x | x  R, x  Q } NOT roots of any polynomial with rational coefficients

8 7/2/2013 Numbers 8 Scientific Notation Standard notation 38100059018442 –60850017290000.00049487173 –0.2974615490024 Scientific notation 3.8100059018442 x 10 13 –6.085001729 x 10 13 4.9487173 x 10 – 4 –2.974615490024 x 10 – 1

9 7/2/2013 Numbers 9 General form For real number r, scientific notation is r = c x 10 n where n is an integer and 1 ≤  Constant c usually a single-digit integer Scientific Notation c < 10

10 7/2/2013 Numbers 10 Think about it !


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