Write the fraction as a decimal.

Lesson 9.2, For use with pages 475-480

1. 45

2. 59

ANSWER 0.8

Write the fraction as a decimal.

Lesson 9.2, For use with pages 475-480

1. 45

2. 59

ANSWER 0.5

RATIONAL and IRRATIONALNUMBERS

9.2

Essential Questions

What is the difference between an irrational number and a rational number?

How are real numbers and the Pythagorean Theorem used in everyday life?

What types of real-life situations could the Pythagorean Theorem or square roots apply to? Why?

Rational Numbers

Rational numbers are simply numbers that can be written as fractions or ratios

The hierarchy of real numbers looks something like this:

1, 2, 3, 4, etc.

0, 1, 2, 3, 4, 5

.. –2, –1, 0, 1, 2, .

Rational and irrational numbers

Can be written as a fractionCan’t be written as a fraction

Rational Numbers: Any number that can be written in fraction form is a rational number. This includes integers, terminating

decimals, and repeating decimals as well as fractions.

An integer can be written as a fraction simply by giving it a denominator of one, so any integer is a rational number.

A terminating decimal can be written as a fraction simply by writing it the way you say it: 3.75 = three and seventy-five hundredths =

So, any terminating decimal is a rational number.

A repeating decimal can be written as a fraction using algebraic methods, so any repeating decimal is a rational number.

Irrational Numbers A number that cannot be expressed as

a repeating or terminating decimal. An integer that is not a perfect square

has an irrational root.

REALS (the real numbers) The rational and irrational numbers.

Rational Number

Fractions Ratios Whole numbers Integers Terminating

decimals (stop) Repeating decimals Square root of a

perfect square

Irrational Numbers

Non-terminating decimal

Non-repeating decimal

Square root of a number that is not a perfect square

GUIDED PRACTICE for Example 1

Tell whether the number is rational or irrational. Explain your reasoning.

5 8

1.

GUIDED PRACTICE for Example 1

Tell whether the number is rational or irrational. Explain your reasoning.

5 8

1.

Rational because if we write it in its decimal form then it would be 0.625 which is terminating so it is a rational number

ANSWER

GUIDED PRACTICE for Example 1

Tell whether the number is rational or irrational. Explain your reasoning.

2. 7

GUIDED PRACTICE for Example 1

Tell whether the number is rational or irrational. Explain your reasoning.

2.

ANSWER

Irrational because it is not a perfect square

2.64579131 . . . .

7

GUIDED PRACTICE for Example 1

Tell whether the number is rational or irrational. Explain your reasoning.

3. 25

GUIDED PRACTICE for Example 1

Tell whether the number is rational or irrational. Explain your reasoning.

3.

ANSWER

Rational because it is a perfect square

25

GUIDED PRACTICE for Example 1

Tell whether the number is rational or irrational. Explain your reasoning.

4. 29

GUIDED PRACTICE for Example 1

Tell whether the number is rational or irrational. Explain your reasoning.

4. 29

ANSWER

Rational because if we write it in its decimal from then it would be 0.2 where 2 repeating so it is a rational number

EXAMPLE 1

Number

a. 3 4

b. 111

c. 3

Rational

Rational

Irrational

Terminating

Repeating

Non terminating and non repeating

111 = 0.0909… = 0.09

3 = 1.7320508 . . .

34 = 0.75 3

Classifying Real Numbers

Type Decimal Form Type of Decimal

Examples Which of the following are irrational numbers?

1. 167

2. 900

3. 5476

4. 59841

1. Irrational

2. Rational -30

3. Rational 74

4. Irrational

Homework

Page 477 #1-15 Problems 3-14 will be two points each

One point for rational or irrational One point for the reason