The Real Numbers 3-7 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

The Real Numbers 3-7 Warm Up Each square root is between two integers. Name the two integers. Use a calculator to find each value. Round to the nearest tenth. 10 and 11 –4 and –3 1.4 – – – 123

The Real Numbers 3-7 Problem of the Day The 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

The Real Numbers 3-7 Learn to determine if a number is rational or irrational.

The Real Numbers 3-7 irrational number real number Density Property Vocabulary

The Real Numbers 3-7 Animals Vertebrates Biologists classify animals based on shared characteristics. The cardinal is an animal, a vertebrate, a bird, and a passerine. You already know that some numbers can be classified as whole numbers, integers, or rational numbers. Birds Passerines

The Real Numbers 3-7 Recall that rational numbers can be written as fractions. Rational numbers can also be written as decimals that either terminate or repeat. 3 = = = 1.2

The Real Numbers 3-7 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!

The Real Numbers 3-7 The set of real numbers consists of the set of rational numbers and the set of irrational numbers.

The Real Numbers 3-7 Additional Example 1: Classifying Real Numbers Write all names that apply to each number. 5 is a whole number that is not a perfect square. 5 irrational, real –12.75 is a terminating decimal. –12.75 rational, real 16 2 whole, integer, rational, real = = A. B. C.

The Real Numbers 3-7 Check It Out: Example 1 Write all names that apply to each number. 9 whole, integer, rational, real –35.9 is a terminating decimal. –35.9 rational, real 81 3 whole, integer, rational, real = = A. B. C. 9 = 3

The Real Numbers 3-7 State if each number is rational, irrational, or not a real number. 21 irrational 0303 rational 0303 = 0 Additional Example 2: Determining the Classification of All Numbers A. B.

The Real Numbers 3-7 not a real number Additional Example 2: Determining the Classification of All Numbers – rational 2323 = C. D. State if each number is rational, irrational, or not a real number.

The Real Numbers is a whole number that is not a perfect square. 23 irrational 9090 undefined, so not a real number Check It Out: Example 2 A. B. State if each number is rational, irrational, or not a real number.

The Real Numbers 3-7 not a real number – rational 8989 = C. D. Check It Out: Example 2 State if each number is rational, irrational, or not a real number.

The Real Numbers 3-7 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.

The Real Numbers 3-7 Additional Example 3: Applying the Density Property of Real Numbers ÷ There are many solutions. One solution is halfway between the two numbers. To find it, add the numbers and divide by 2.5 = 6 ÷ = 7 ÷ 2 = Find a real number between 3 and A real number between 3 and 3 is

The Real Numbers 3-7 Check It Out: Example ÷ There are many solutions. One solution is halfway between the two numbers. To find it, add the numbers and divide by 2.7 = 8 ÷ = 9 ÷ 2 = Find a real number between 4 and A real number between 4 and 4 is

The Real Numbers 3-7 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

The Real Numbers 3-7 Lesson Quiz Write all names that apply to each number – State if each number is rational, irrational, or not a real number Find a real number between –2 and – not a real number rational real, irrational real, integer, rational Possible answer –

The Real Numbers Identify all names that apply to. A. real, irrational B. real, rational C. not real, irrational D. not real, rational Lesson Quiz for Student Response Systems

The Real Numbers Identify the name that applies to. A. irrational B. rational C. not a real number D. none Lesson Quiz for Student Response Systems

The Real Numbers Identify a real number between. A. –4 B. C. D. Lesson Quiz for Student Response Systems