1. Objective
Classify Real Numbers

2. Two Kinds of Real Numbers
Rational Numbers
Irrational Numbers

3. Branching Real Numbers
Rational Irrational
Now let’s break these subsets down further!

4. The Real Number System Real Numbers Rational Numbers:
Can be written as a Ratio (fraction) of two integers.
Irrational
Numbers:
Cannot be
written as
a ratio (fraction) of two
integers.
Integers: {…-2,-1,0,1,2,…}
Whole Numbers:
{0,1,2,3,…}
As we build this diagram, we discuss the types of numbers and relate it back to the video if applicable.
Natural Numbers:
{1,2,3,…}

5. Placing Numbers Correctly√2
8/ 2 π
-√225 -1
3/4 1 29 √9
Real Numbers
Rational Numbers
Irrational
Numbers
Integers
Whole Numbers
Natural Numbers

6. How are natural numbers and whole number different?
Contrast…
How are natural numbers and whole number different?
WHole numbers include 0

7. How are natural numbers and whole number different?
Contrast…
How are natural numbers and whole number different?
WHole numbers include 0

8. How are natural numbers and whole number different?
Contrast…
How are natural numbers and whole number different?
WHole numbers include 0

9. How are integers and rational numbers different?
Contrast
How are integers and rational numbers different?
Integers do not include fractions

10. How are natural numbers and whole number different?
Contrast…
How are natural numbers and whole number different?
WHole numbers include 0

11. Examples of Rational Numbers16
1/2
3.56 -8
1.3333…
- 3/4
Can you write 16 as a ratio?
Now try writing -8 as a ratio!

12. Examples of Irrational Numbers
ALL NON-PERFECT ROOTS Pi 17 3 30 π
What is another non-perfect root?

13. Rational & Irrational Numbers
real, rational, integer

14. Rational & Irrational Numbers
real, rational
Rational

15. Rational Rational & Irrational Numbers
real, rational, integer, whole, natural

16. Rational & Irrational Numbers
real, rational
Rational

17. Rational Rational & Irrational Numbers
real, rational, integer, whole, natural

18. Rational & Irrational Numbers
real, rational, integer, whole

19. Rational & Irrational Numbers
NOT EVEN A REAL NUMBER
not real

20. Exit Ticket Write a number that is a rational number
but not an integer.
2. Identify the all the categories for the following numbers -7
…..

21. Rational Numbers
A rational number is a real number that can be written as a fraction of two integers.
When written as a decimal:
The decimal ends OR
The decimal repeats the same exact digit/s (bar notation)

22. How to identify Rational Numbers
Integers and whole numbers
Fractions of 2 integers
Decimals that end
Decimals that don’t end BUT repeat the same exact pattern
Perfect Roots!! (i.e. square roots, cube roots…)

23. Irrational Numbers
An irrational number is a number that cannot be written as a fraction of two integers.
When written as a decimal:
The decimal never ends! AND
The decimal does NOT have a repeating pattern.

24. How to identify Irrational Numbers
Decimals that go on forever with NO repeating pattern.
Non-Perfect Roots!!

25. TRUE
TRUE OR FALSE
When dividing a rational number by a rational number you will always get a rational number.
(A RATION OF 2 INTEGERS)

26. RATIONAL ÷ RATIONAL
7÷8=
0.875
RATIONAL
1 2 ÷ 2 5 =
5 4 or 1.25
RATIONAL
÷ 8.2 =
56.177
RATIONAL

27. TRUE
TRUE OR FALSE
When dividing an irrational number by a rational number you will always get an irrational number.
Both have negative, positive, and zero

28. 7÷ 5 = 3.130495168… 4÷𝜋 = 1.27323954…. IRRATIONAL ÷ RATIONAL
7÷ 5 = …
IRRATIONAL
4÷𝜋 = ….
IRRATIONAL

29. FALSE
TRUE OR FALSE
When dividing an irrational number by a irrational number you will always get an irrational number.
Both have negative, positive, and zero

30. IRRATIONAL ÷ IRRATIONAL
𝜋 𝜋 =
RATIONAL 1 =
1 2
RATIONAL = ….
IRRATIONAL

31. RATIONAL AND IRRATIONAL
RATIONAL + - x ÷ RATIONAL = RATIONAL
RATIONAL + - x ÷ IRRATIONAL = IRRATIONAL
IRRATIONAL + - x ÷ IRRATIONAL = DEPENDS!!!
USUALLY IRRATIONAL
SOMETIMES THEY SIMPLIFY TO A RATIONAL

32. IRRATIONAL ÷ IRRATIONAL
𝜋 𝜋 =
RATIONAL 1 =
1 2
RATIONAL = ….
IRRATIONAL

33. Rational & Irrational Numbers2
real
Irrational

34. Rational & Irrational Numbers
169
real
Rational

35. Rational & Irrational Numbers
3 −27 -3
Rational

36. Rational & Irrational Numbers
3 200 -3
Irrational

37. Rational & Irrational Numbers
− 36
Rational
real

38. Rational & Irrational Numbers10
Irrational
real

39. Rational & Irrational Numbers
6 8
real
Irrational

40. 4𝜋 7𝜋 Rational Rational & Irrational Numbers
real, rational, integer, whole, natural
Rational

41. Rational & Irrational Numbers
6 − 6
Rational
real, rational

42. Rational & Irrational Numbers
6 + 6
Irrational
real, rational

43. Rational & Irrational Numbers
𝜋 𝜋−1
real, rational

44. Rational & Irrational Numbers…
Irrational
6/7

45. Rational & Irrational Numbers…
Rational
6/7

46. 0.93744802 Rational IT ENDS Rational & Irrational Numbers
There is no … so it ends!
IT ENDS

47. Rational & Irrational Numbers…
Rational
6/7