each square root is between two integers. name the two integers. use a calculator to find each...

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

–11.1

1. 119

2. – 15

3. 2

4. – 123

Before the Bell3-7

Today’s learning Target:

3-7

I can •Classify (name) numbers•Determine if a number is rational or irrational.

Rational number

Vocabulary

1, 2, 3, 4, 5…

3-7

Real Numbers:Natural Numbers

Whole Numbers

Integers

Irrational number

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 = 3.84 5

= 0.623

1.44 = 1.2

The set of real numbers consists of the set of rational numbers and the set of irrational numbers.

3-7 Vocabulary

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.–12.75rational, real

16 2

Natural, whole, integer, rational, real

= = 24 2

16 2

1.

2.

3.

I’ll show you.3-7

Write all names that apply to each number.

9

Natural, whole, integer, rational, real

–35.9 is a terminating decimal.–35.9rational, real

81 3

natural, whole, integer, rational, real

= = 39 3

81 3

4.

5.

6.

9 = 3

Try this with a partner.3-7

State if each number is rational, irrational, or not a real number.

21

irrational

0 3

rational

0 3

= 0

7.

8.

I’ll show you.3-7

not a real number

–4

4 9

rational

2 3

9.

10.

State if each number is rational, irrational, or not a real number.

Try this with a partner.3-7

23 is a whole number that is not a perfect square.

23

irrational

9 0

undefined, so not a real number

11.

12.

State if each number is rational, irrational, or not a real number.

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.

Additional Example 3: Applying the Density Property of Real Numbers

2 5

3 + 3 ÷ 23 5

There are many solutions. One solution is halfway between the two numbers. To find it, add the numbers and divide by 2.

5 5

= 6 ÷ 21 2

= 7 ÷ 2 = 3

31 2

3 3 31 5

2 5 43 33

54 5

Find a real number between 3 and 3 .

3 5

2 5

A real number between 3 and 3 is 3 .3 5

2 5

1 2

Lesson Quiz

Write all names that apply to each number.

1. 2. –

State if each number is rational, irrational, or not a real number.

3. 4.

2

4 • 9

16 2

25 0

not a real number rational

real, irrational real, integer, rational

Did you master today’s learning target?3-7

Assignment:

Lesson 3-7

Page 125, problems 31-47, 57

3-7