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Math 8 SOL 8.2 (3-3 5-2 9-2) Real Numbers NOTES Ms. Graham/Mr. Barlock Name: _______________________________ Block: _______ Date: _____________ WARM UP 1. Write down where you were born. 2. Write your name in the circle that best describes that place (be as specific as possible). Loudoun Co VA Earth USA NOTES In the English language, the words rational and irrational mean: Rational: Irrational: Set Terms: Term Definition A collection of objects A member of the set A set containing one or more elements of a parent set. Every element of a subset is contained in the parent set Math 8 SOL 8.2 (3-3 5-2 9-2) Real Numbers NOTES Ms. Graham/Mr. Barlock Example: S= {yellow, red, blue, green} Elements: A subset of S: Real Number Subsets: Subset name: Set: Symbol Natural Numbers { } Whole Numbers { } Integers { } Rational Numbers { } Irrational Numbers { } REAL NUMBERS Sort the numbers below in to the most specific real number subset: -4 0 2 1 3 0.09 Math 8 SOL 8.2 (3-3 5-2 9-2) Real Numbers NOTES 2 Example Natural Whole Ms. Graham/Mr. Barlock 1. 8 Integer 0.02345… 25 Rational Irrational Real -4 0 2 1 3 0.09 2 1. 8 25 0.02345… Rational Numbers: Definition: A rational number is a number that can be written as a fraction in the form ___, where a and b are integers and b ______. ** If a number can be written as a fraction, it is rational. Decimals that do not terminate or do not repeat cannot be written as fractions, so they are NOT rational. ** Writing integers and mixed numbers as fractions: Integers can be made into fractions by using the integer as the numerator and _______ as the denominator. Ex: 3 = Math 8 SOL 8.2 (3-3 5-2 9-2) Real Numbers NOTES Ms. Graham/Mr. Barlock Mixed numbers can be converted to ________________ fractions. Examples – write as fractions: a) 275 b) -24 c) 5 2 3 d) 1 1 4 Writing Decimals as Fractions: Three Possibilities: Decimal _________________ Example: __________ Decimal _________________ Example: __________ Decimal neither ______________ or _______________ Example: __________ Writing terminating decimals as fractions: Turn the decimal into a fraction: “Read it, write it, reduce it.” Examples – write the following decimal numbers as fractions: a) 0.5 b) 0.48 c) 3.25 d) 1.125 Writing repeating decimals as fractions: Write 0 .8 as a decimal SHORTCUT METHOD: 1) Let N = the number (decimal): N = 0.888888… 2) Multiply each side by 10 10N = 8.8888888… 3) Subtract N - N = 0.8888888… 9N = 8 4) Divide N = ______ 1) Pretend the _______ isn’t there; write as a ____________: 0.8 = 2) Subtract 1 from the denominator: 0 .8 =_____ Examples – write each repeating decimal as a fraction: a) .5 b) 2 .25 c) 5 .6 d) 0 .32 8 10