Presentation on theme: "Warm Up Problem of the Day Lesson Presentation Lesson Quizzes."— Presentation transcript:
1 Warm UpProblem of the DayLesson PresentationLesson Quizzes
2 Warm UpEach square root is between two integers. Name the two integers.Use a calculator to find each value Round to the nearest tenth.10 and 112. – 15–4 and –31.44. – 123–11.1
3 Problem of the DayThe circumference of a circle is approximately 3.14 times its diameter. A circular path 1 meter wide has an inner diameter of 100 meters. How much farther is it around the outer edge of the path than the inner edge?6.28 m
4 Sunshine State Standards MA.8.A.6.2 …Compare mathematical expressions involving real numbers and radical expressions.
6 Biologists classify animals based on shared characteristics Biologists classify animals based on shared characteristics. The cardinal is an animal, a vertebrate, a bird, and a passerine.AnimalsYou already know that some numbers can be classified as whole numbers, integers, or rational numbers.VertebratesBirdsPasserines
7 Recall that rational numbers can be written as fractions and as decimals that either terminate or repeat.4 5233 = 3.8= 0.61.44 = 1.2
8 Irrational numbers can only be written as decimals that do not terminate or repeat. If a whole number is not a perfect square, then its square root is an irrational number.2 ≈ …A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.Caution!
9 The set of real numbers consists of the set of rational numbers and the set of irrational numbers.
10 Additional Example 1: Classifying Real Numbers Write all names that apply to each number.A.55 is a whole number that is not a perfect square.irrational, realB.–12.75–12.75 is a terminating decimal.rational, real16 2= = 24 216 2C.whole, integer, rational, real
11 Write all names that apply to each number. Check It Out: Example 1Write all names that apply to each number.A.99 = 3;natural, whole, integer, rational, real3 5B.–rational, realC.3.724rational, real
12 Additional Example 2: Determining the Classification of All Numbers State if each number is rational, irrational, or not a real number.0 30 3= 0A.rationalB.–4not a real number
13 Additional Example 2: Determining the Classification of All Numbers State if each number is rational, irrational, or not a real number.4 92 3=4 9C.rational
14 Check It Out: Example 2State if the number is rational, irrational, or not a real number. Justify your answer.A.–7√–7 is not a real number because it is the square root of a negative number.6 0B.––6 0is not a real number because division by 0 is notdefined.
15 Check It Out: Example 2State if the number is rational, irrational, or not a real number. Justify your answer.C.√59 + 5√59 + 5= √64 = 8 is a rational number.
16 The Density Property of real numbers states that between any two real numbers is another real number. This property is also true for rational numbers, but not for whole numbers or integers. For instance, there is no integer between –2 and –3.
17 Additional Example 3: Applying the Density Property of Real Numbers Find a real number between and3 52 5There are many solutions. One solution is halfway between the two numbers. To find it, add the numbers and divide by 2.2 5÷ 23 55 5= ÷ 21 2= 7 ÷ 2 = 331 52 543 54 531 2A real number between and is 3 .3 52 51 2
18 Check It Out: Example 3Find a real number between and2 81 81 21 82 883 8=1 283 8=3 16= 53 16Possible answer:5
19 Lesson Quiz for Student Response Systems Lesson QuizzesStandard Lesson QuizLesson Quiz for Student Response Systems1919
20 Lesson QuizWrite all names that apply to each number.1.22. –16 2real, irrationalreal, integer, rationalState if each number is rational, irrational, or not a real number. Justify your answer.25 04.3.4 • 9not a real number; by 0rational;2 3 is 65.Find a real number between –2 and –2 .3 83 4Possible answer –2 .5 8
21 Lesson Quiz for Student Response Systems 1. Identify all names that apply toA. real, irrationalB. real, rational C. not real, irrationalD. not real, rational2121
22 Lesson Quiz for Student Response Systems 2. Identify the name that applies toA. irrationalB. rational C. not a real numberD. none2222
23 Lesson Quiz for Student Response Systems 3. Identify a real number betweenA. –4B. C.D.2323