Choosing the Right CBSE School A Comprehensive Guide for Parents
Rational numbers
1. Introduction to Real NumbersIntroduction to Real Numbers
andand
Their PropertiesTheir Properties
2. Two Kinds of Real Numbers
• Rational Numbers
• Irrational Numbers
3. 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.
5. 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.
7. What are integers?
• Integers are the
whole numbers and
their opposites.
• Examples of integers
are
6
-12
0
186
-934
8. Using Exponents
If “a” is a real number and “n” is a natural number, then an
=
a•a•a•••a•a (n factors of a).
where n is the exponent, a is the base, and an
is an
exponential expression. Exponents are also called powers.
To find the value of a whole number exponent:
100
= 1, 20
= 1, 80
= 1, #0
= 1
101
= 10, 21
= 2, 81
= 8, #1
= #
102
= 10 x 10 = 100, 22
= 2 x 2 = 4, 82
= 8 x 8 = 64
103
= 10 x 10 x 10 = 1000, 23
= 2 x 2 x 2 = 8
104
= 10 x 10 x 10 x 10 = 10,000 24
= 2 x 2 x 2 x 2 = 16
(-10)3
= (-10)(-10)(-10) (12).5
=
9. Using the Identity Properties
“additive identity”
Zero is the only number that can be added to
any number to get that number.
0 is called the “identity element for addition”
a + 0 = a Example 1: 4 + 0 = 4
“multiplicative identity”
One is the only number that can be multiplied
by any number to get that number.
1 is called the “identity element for
multiplication”
a • 1 = a Example 2: 4 • 1 = 4
10. The Real Number SystemThe Real Number SystemReal Numbers
Rational Numbers Irrational Numbers
3
1/2
-2
15%
2/3
1.456
-
0.7
0
√3 2
π
−√5
2
3π
4
11. The Real NumberThe Real Number
SystemSystem Real Numbers
Rational Numbers Irrational Numbers
31/2 -2
15
%
2/3
1.45
6
-
0.7
0
√3 2
π
−√5
2
3π
4
Integers
12. The Real Number System
Real Numbers
Rational Numbers Irrational Numbers
31/2
-2
15
%
2/3
1.45
6
-
0.7
0
√3 2
π
−√5
2
3π
4
Integers
Whole
13. The Real Number System
Real Numbers
Rational Numbers Irrational Numbers
3
1/2
-2
15
%
2/3
1.45
6
-
0.7
0
√3 2
π
−√5
2
3π
4
Integers
Whole
Natural
14. Finding Additive inversesFinding Additive inverses
For any real number x, the number –x is theFor any real number x, the number –x is the
additive inverse of x.additive inverse of x.
Example 1:Example 1:
Number
Inverse
Additive
6 - 6
- 4 4
- 8.7 8.7
0 0
2
3
2
3
−
15. Symbol Meaning Example
= is equal to 4 = 4
≠ is not equal to 4 ≠ 5
< is less than 4 < 5
≤ is less than or equal -4 ≤ -3
> is greater than -4 > -5
≥ is greater than or equal -8 ≥ - 10