150ch1_1-2 - Math 150, Fall 2007, c Benjamin Aurispa...

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Math 150, Fall 2007, c ± Benjamin Aurispa Chapter 1: Fundamentals 1.1 Real Numbers Types of Real Numbers: Natural Numbers: { 1 , 2 , 3 ,... } ; These are the counting numbers. Integers: { ... - 3 , - 2 , - 1 , 0 , 1 , 2 , 3 ,... } ; These are all the natural numbers, their negatives, and 0. Rational Numbers: { m n | n,m are integers ,n 6 = 0 } ; These are ratios of integers (fractions). All numbers with repeating decimals can be written as fractions. Irrational Numbers: These are the nonrepeating, nonterminating numbers. Ex: π, 2 , 3 4 ,... Real Numbers: All of the above put together. Example: Consider the list of numbers 12, 1 . 987, - 5 2 , π 4 , - 4, - 7 5, 0, 2 . 5 7. List the numbers that are: natural numbers integers rational numbers irrational numbers Since all repeating decimals can be converted into fractions, how can we do this? The idea is to first count how many digits are repeated and then to multiply by this power of 10. Examples: 1. Convert x = 0 . 57 into a fraction. 2. Convert x = 0 . 2 3 into a fraction. 1
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Math 150, Fall 2007, c ± Benjamin Aurispa Properties of Real Numbers Commutative Property: a + b = b + a , ab = ba Associative Property: a + ( b + c ) = ( a + b ) + c , a ( bc ) = ( ab ) c Distributive Property: a ( b + c ) = ab + ac , ( a + b ) c = ac + bc Example: Write (2 x - 3)4 without parentheses. Some Properties of Negative Numbers
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150ch1_1-2 - Math 150, Fall 2007, c Benjamin Aurispa...

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