1. 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.
10 and 11
2. – 15
–4 and –3
1.4
4. – 123
–11.1

2. 3-7 Today’s learning Target: I can Classify (name) numbers
Determine if a number is rational or irrational.

3. 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

4. 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

5. 3-7
Vocabulary
The set of real numbers consists of the set of rational numbers and the set of irrational numbers.

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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.

12. Additional Example 3: Applying the Density Property of Real Numbers
Find a real number between and
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
÷ 2
3 5
5 5
= ÷ 2
1 2
= 7 ÷ 2 = 3 3
1 5
2 5 4
3 5
4 5 3
1 2
A real number between and is 3 .
3 5
2 5
1 2

13. 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

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