1. Warm-Up #12 (Monday, 9/28)
3 ∙ 27
3 5 ∙
3 5 (2 5 − 125)

2. Homework (Monday, 9/28)
Lesson 1.05 packet

3. Lesson 1.05 Rational and Irrational Numbers

4. My Thinking Process

5. Two Kinds of Real Numbers
Rational Numbers
Irrational Numbers

6. Rational Numbers
A rational number is a real number that can be written as a ratio of two integers.
A rational number written in decimal form is terminating or repeating.

7. Examples of Rational Numbers16
1/2
3.56 -8
1.3333…
- 3/4

8. Irrational Numbers
An irrational number is a number that cannot be written as a ratio of two integers.
Irrational numbers written as decimals are non-terminating and non-repeating.

9. Examples of Irrational Numbers
Square roots of non- perfect “squares”
Pi= 3.14… 17

10. What are integers?
Integers are the whole numbers and their opposites. Integers are rational numbers because they can be written as fraction with 1 as the denominator.
Examples of integers are 6
-12
186
-934

12. Rational and Irrational Numbers
Example questions
Show that
is rational a
rational
Show that
is rational b
rational

13. Rational and Irrational Numbers
Questions
State whether each of the following are rational or irrational. a b c d
irrational
rational
rational
irrational e f g h
irrational
rational
rational
rational

14. Rational and Irrational Numbers
Combining Rationals and Irrationals
Determine whether the following are rational or irrational.
(a) (b) (c) 0.666… (d) (e)
rational
irrational
rational
rational
irrational
(f) (g) (h) (i) (j)
irrational
irrational
rational
rational
irrational
(j) (k) (l)
irrational
rational
rational