This document defines and provides examples of different types of real numbers including rational numbers, irrational numbers, natural numbers, whole numbers, integers, and their relationships. It discusses how rational numbers can be divided into integers, whole numbers, and natural numbers. Examples are provided to illustrate rational numbers like 1/2 and irrational numbers like the square root of 5. Practice problems ask the learner to identify true/false statements about these number types and determine whether given numbers are rational or irrational.
This is meant for age group 11 to 14 years.
For Class VIII CBSE.
Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
This is meant for age group 11 to 14 years.
For Class VIII CBSE.
Some viewers have requested me to send the file through mail.
So I allowed everybody to download.My request is whenever you are using plz acknowledge me.
Pratima Nayak ,Teacher,Kendriya Vidyalaya,Fort William,Kolkata
pnpratima@gmail.com
Based on Text book
The real numbers are the set of numbers containing all of the rational numbers and all of the irrational numbers. The real numbers are “all the numbers” on the number line. There are infinitely many real numbers just as there are infinitely many in the other sets of numbers.
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3. Objectives
1. Define and recognize:
rational numbers and irrational numbers,
natural numbers,
whole numbers and
integers.
2. List the numbers belonging to any subsets of R
3. State the relationship among sets of numbers.
6. Manual of this tutorial!
This tutorial is designed to teach you about Real numbers.
The presentation starts with notes and examples followed
by practice problems.
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8. Naturals Numbers
Type of Definition Examples
Number
Natural The set of counting 1
Number numbers which is 24/4
also a subset of 3
N
real number √16
343
9. Whole Numbers
Type of
Definition Examples
Number
Whole 0
The set of natural
1
Number numbers plus a “0”
3
W W = {0,1,2,3,4,…} √16
343
10. Integers
Type of
Definition Examples
Number
The set of natural -√16
Integer
numbers, their -2
Z negatives and 0 0
Z={…,-3,-2,-1,0,1,2,3,…} 24/4
343
11. Rational Numbers
Type of
Number Definition Examples
A subset of real
Rational number that can be -1
Number written as a quotient ⅝
p/q where p, q ε Z -10.45
Q
and q ≠ 0 3.1414…
Q = {p/q |p, q ε Z, q ≠ 0} 5 - 43
12. Irrational Numbers
Type of
Definition Examples
Number
A subset of real
Irrational numbers that are not e
Number rational or numbers √2
whose decimal parts π
Q’ 3√(-12)
neither repeat nor
terminate. -7.4512…
13. Real Numbers Real
Numbers (R)
Rational Irrational
Real numbers can be Numbers Numbers
(Q) (Q’)
divided into two basic
groups: Irrational
numbers and Rational Integers (Z)
numbers.
Whole
Rational Numbers can Numbers
(W)
further be divided into 3
groups: integers, whole
Natural
numbers, and natural Numbers
numbers. (N)
14. Sets of numbers
Q 1/2, R
Z -1,-2..
W 0
Q’
N
1,2,3.. ∏ (pi)
√5
∴ Q ∪ Q' = R
15. Practice 1
Determine whether each statement is TRUE or FALSE.
1. Every counting number is an integer. True
2. Zero is a counting number. False
3. Negative six is greater than negative three. False
4. Some of the integers is natural numbers. True
16. Practice 2
Which of the following
A -1/2
numbers is irrational?
B 3.63
C 121
D 3
37
