3-7 Before the Bell Each square root is between two integers. Name the two integers. Use a calculator to find each value. Round to the nearest tenth. 1. 119 10 and 11 2. – 15 –4 and –3 3. 2 1.4 4. – 123 –11.1

3-7 Today’s learning Target: I can Classify (name) numbers Determine if a number is rational or irrational.

Vocabulary 3-7 Real Numbers: Natural Numbers 1, 2, 3, 4, 5… Whole Numbers 0, 1, 2, 3, 4, 5… Integers … -3, -2, -1, 0, 1, 2, 3, 4, 5… Rational number - any number that can be written as a ratio (or fraction) - They never end or repeat. Irrational number

Recall that rational numbers can be written as fractions Recall that rational numbers can be written as fractions. Rational numbers can also be written as decimals that either terminate or repeat. 4 5 23 3 = 3.8 = 0.6 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 5 is a whole number that is not a perfect square. irrational, real 2. –12.75 –12.75 is a terminating decimal. rational, real 16 2 = = 2 4 2 16 2 3. 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. –35.9 –35.9 is a terminating decimal. rational, real 81 3 = = 3 9 3 81 3 6. 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 0 3 0 3 = 0 8. rational

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 4 9 2 3 10. rational

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 9 0 12. 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 Find a real number between 3 and 3 . 3 5 2 5 There are many solutions. One solution is halfway between the two numbers. To find it, add the numbers and divide by 2. 2 5 3 + 3 ÷ 2 3 5 5 5 = 6 ÷ 2 1 2 = 7 ÷ 2 = 3 3 1 5 2 5 4 3 5 4 5 3 1 2 A real number between 3 and 3 is 3 . 3 5 2 5 1 2

Did you master today’s learning target? 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, irrational real, integer, rational State if each number is rational, irrational, or not a real number. 25 0 4. 3. 4 • 9 not a real number rational

Lesson 3-7 Page 125, problems 31-47, 57 Assignment: 3-7 Lesson 3-7 Page 125, problems 31-47, 57