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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 Bell 3-7

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Page 1: 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

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

Page 2: 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

Today’s learning Target:

3-7

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

Page 3: 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

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.

Page 4: 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

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

Page 5: 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

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

3-7 Vocabulary

Page 6: 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

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

Page 7: 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

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

Page 8: 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

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

Page 9: 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

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

Page 10: 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

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

Page 11: 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

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.

Page 12: 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

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

Page 13: 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

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

Page 14: 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

Assignment:

Lesson 3-7

Page 125, problems 31-47, 57

3-7


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