Prompt, complete, accurate and self-explanatory visual presentation of the concepts of various types of numbers and number line. A brief description of numbers with diagrammatic representation so that students can understand. How these numbers can be represented on the number line.
9. Number Systems
INTEGERS can be…
Negative Integers e.g. -1, -2, -3, -4,…
Non Negative Integers e.g. 0, 1, 2, 3, 4,…
Positive Integers e.g. 1, 2, 3, 4, 5, 6, 7, 8,…
9
10. Number Systems
Denoted by ‘r’ are numbers which
can be written in p/q form, where
p and q are integers and q≠ 0.
Rational Numbers
Example
Collection of rational number is
denoted by “Q”
10
RationalNumbers
11. 11
Number Systems
Some Important Points:-
Every integer, whole and natural number is a rational number.
Number of rational numbers between two rational numbers is
infinite.
Suppose a and b are two rational numbers, then
a x b
a + b = Rational Number
a + b
a ÷ b (where b is non-zero i.e. b ≠ 0)
Closure property under addition, subtraction, multiplication and
division is satisfied by rational numbers.
RationalNumbers
12. Number Systems
Irrational Numbers
All numbers which cannot be written
in p/q form, where p and q are
integers and q≠ 0
IrrationalNumbers
Example
12
Square roots of all positive integers are not irrational e.g.
9 = 3 (rational number)
13. 13
Number Systems
Some Important Points:-
Irrational numbers have non-terminating and non-repeating
decimal expression.
Irrational numbers can be easily represented on number line by
using Pythagoras Theorem where
In right angled ∆[Hypotenuse]2 = [Base]2 + [Perpendicular]2
Suppose a and b are two irrational numbers, then
a x b
a + b = Not always an Irrational Number
a + b
a ÷ b
Closure property under addition, subtraction, multiplication and
division is not satisfied by irrational numbers.
Irrational Numbers
14. 14
RATIONAL NUMBER
TERMINATING or NON-
TERMINATING RECURRING
DECIMAL EXPANSION DECIMAL EXPANSION
IRRATIONAL NUMBER
NON-TERMINATING or
NON-RECURRING
DECIMAL EXPANSION DECIMAL EXPANSION
Number Systems
Decimal Expansion
15. 15
Number Systems
Real Numbers
Real numbers include all rational and all
irrational numbers. Denoted by ‘R’
RealNumbers
THE REAL NUMBER LINE
17. 17
Number Systems
RealNumbers
Real Numbers :-
Both rational and irrational numbers together makes a collection
of real numbers.
On a number line, there is a unique real number corresponding to
every point and also corresponding to each real number there is a
unique point.
Suppose we have one rational and one irrational number, then:-
Rational Number + Irrational Number = Irrational Number
Rational Number - Irrational Number = Irrational Number
Rational Number x Irrational Number = Irrational Number, Rational
Number ≠ 0
Rational Number / Irrational Number = Irrational Number, Rational
Number ≠ 0
Real numbers also satisfy the various laws i.e. commutative,
associative and distributive laws etc.
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Number Systems
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