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Rational/ Irrational #’s Absent Copy Thurs/Fri 3/7,8 Whole #’s Integers Rational #’s Counting #’s and zero 0,1,2,3,4,5……….. neg. and pos. numbers and 0 -5,-4,-3,-2,-1,0,1,2,3,4,5…….. Terminating/repeating decimals 0.5, 1.45, 3.9 .3333, 3.151515, Fractions (that terminate or repeat) /perfect squares 1 √25, √81, 2 , 3 4 Rational #’s include: All integers, all fractions and decimals that end or repeat Rational #’s 0 .3 3 1 5 Integers 100 30.3 0.3 Whole #s 6 3 0 .4 2 5 11 2 2 Irrational #’s include: Decimals that do not end or repeat and square roots that are not perfect squares. 1. .1823456…….., √3 = 1.732050807 Real Numbers Rational and irrational #’s Non – Real #’s 16 and 7 0 Example 1 • Write all classifications that apply to this #. -8 10 • This is a fraction. • This # is also a? • It is also a Terminating decimal. .80 10 8.00 -80 00 Fraction, terminating decimal, rational # • This # is a? • Is this # Rational or Irrational Why? It is rational because terminating decimals are rational. Solution Example 2 • Write all classifications • This # is a? • This is a sq. rt. that apply to this #. • What can we do to make this sq. rt. More 32 simple to solve? 2 • We can divide 32 by 2 and get 16. • This # is also an? 16 • This is also a whole # and an integer. 4 • 4 Factor Factor 4 Whole #, Integer, Rational # Solution • Is this # Rational or Irrational Why? It is rational because integers and whole #’s are part of the rational family. Example 3 • Is this # rational, irrational, or not real. • Is this a perfect square? • Yes it is. - 16 4 • 4 factor • What else can we call this #? • We can call it an integer. factor -4 • Is a perfect square irrational or rational Rational # Solution Example 4 • Is this # rational, irrational, or not real. 5 29 • It is called a fraction. • Is it a repeating decimal or does it terminate or is it a nonrepeating decimal? .1724 29 5.0000 -29 210 -203 70 -58 120 -116 irrational # • What is this # called? • It is a non-repeating decimal. • Is this # irrational or rational Solution