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Transcript
3-7 Before the Bell Each square root is between two integers. Name the two integers. 1. 119 10 and 11 2. – 15 –4 and –3 Use a calculator to find each value. Round to the nearest tenth. 3. 4. – 2 1.4 123 –11.1 3-7 Today’s learning Target: I can • Classify (name) numbers • Determine if a number is rational or irrational. 3-7 Vocabulary Real Numbers: Natural Numbers Whole Numbers Integers Rational number Irrational number 1, 2, 3, 4, 5… 0, 1, 2, 3, 4, 5… … -3, -2, -1, 0, 1, 2, 3, 4, 5… - any number that can be written as a ratio (or fraction) - They never end or repeat. Recall that rational numbers can be written as fractions. Rational numbers can also be written as decimals that either terminate or repeat. 3 4 = 3.8 5 2 = 0.6 3 1.44 = 1.2 3-7 Vocabulary The set of real numbers consists of the set of rational numbers and the set of irrational numbers. 3-7 I’ll show you. Write all names that apply to each number. 1. 5 is a whole number that is not a perfect square. irrational, real 5 2. –12.75 –12.75 is a terminating decimal. rational, real 3. 16 2 16 4 = =2 2 2 Natural, whole, integer, rational, real 3-7 Try this with a partner. Write all names that apply to each number. 4. 9 9 =3 Natural, whole, integer, rational, real 5. 6. –35.9 –35.9 is a terminating decimal. rational, real 81 81 9 = =3 3 3 3 natural, whole, integer, rational, real 3-7 I’ll show you. State if each number is rational, irrational, or not a real number. 7. 21 irrational 8. 0 3 rational 0 =0 3 3-7 Try this with a partner. State if each number is rational, irrational, or not a real number. 9. –4 not a real number 10. 4 9 rational 2 3 3-7 State if each number is rational, irrational, or not a real number. 11. 23 23 is a whole number that is not a perfect square. irrational 12. 9 0 undefined, so not a real number 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. Additional Example 3: Applying the Density Property of Real Numbers 2 3 Find a real number between 3 and 3 . 5 5 There are many solutions. One solution is halfway between the two numbers. To find it, add the numbers and divide by 2. 2 3 5 1 3 +3 ÷2 =6 ÷2 =7÷2=3 5 5 5 2 3 1 2 3 4 3 5 3 5 13 5 35 4 32 3 2 1 A real number between 3 and 3 is 3 . 5 5 2 3-7 Did you master today’s learning target? Lesson Quiz Write all names that apply to each number. 1. 2 2. – 16 2 real, integer, rational real, irrational State if each number is rational, irrational, or not a real number. 3. 25 0 not a real number 4. 4 • rational 9 3-7 Assignment: Lesson 3-7 Page 125, problems 31-47, 57