This document provides an overview of different number systems including decimal, binary, and Mayan systems. It discusses various types of numbers such as natural numbers, integers, rational numbers, and irrational numbers. It also describes properties of numbers including terminating and non-terminating decimals, the number line, and rationalization of expressions involving square roots.

1. THE AMAZING WORLD OF NUMBERS……
BY – LISA MUNDA
CLASS-IX ‘A’

2. Acknowledgement
I would like to thank the Math Department for giving us
an opportunity to express ourselves via mathematical
project. I would also like to thank our computer
teacher to providing us with E-mail ID. Also I thanks
my friends for their ideas provided to me. I am grateful
to all of them.

3. INTRODUCTION
A number system defines a set of values used to
represent a quantity .It is a system of writing
for numbers .It provides a unique
representation to every number and present
the arithmetic and algebraic structure of the
figures .It also allows us to operate arithmetic
operations like addition, subtraction
multiplication and division.

4. NUMBER SYSTEM ACCORDING
TO DIFFERENT
CIVILIZATION....

5. THE DECIMAL NUMBER SYSTEM
 The number system we use on day to day basis in the
decimal system, which is based on ten digits: zero
through nine. As the decimal system is based on ten
digits, it is to be base-10 or radix-10. outside of
specialized requirement such as computing, base-10
numbering system have been adopted almost
universally.

6. Mayan number system
 The system is unique to our current decimal system, as
our current decimal system uses base-10 whereas, the
Mayan Number System uses base-20.
 The Mayan system used a combination of two symbols.
A dot(.) was used to represent the units and a dash(-)
was used to represent five.

7. Binary number system
 The binary number system, or base-2 number system,
represents numeric values using two symbols, 0 and 1.
More specifically, the usual base-2 system is a
positional notation with a radix 2 owing to straight
forwarding implementation in digital electronic a
using logic gates, the binary system is used by all
modern computers.

8. BRIEF INTRODUCTION ABOUT
NUMBERS
A number is a mathematical object used in counting and
measuring . In mathematics, the defination of number
has been extended over the year to include such
numbers as zero, negative numbers, and complex
numbers.
Numbers were probably first used many thousands of
years ago in commerce, and initially only whole
numbers and perhaps rational numbers were needed.
But already in Babylonian times, practical problems of
geometry began to require square roots.

9. TYPES OF
NUMBERS…….

10. NATURAL NUMBERS
 The most familiar numbers are the natural numbers or
counting number: one, two, three and so on……
 Properties of the natural numbers related to
divisibility, such as the distribution of prime numbers,
are studied in number theory. The natural numbers
had their origins in the words used to count things,
beginning with the number one.

11. Whole numbers
Whole number is collection of positive numbers and
zero. The whole number is represented as{0,1,2,3,4…..}.
The set of whole numbers may be finite or infinite.
Infinite set means the numbers are uncountable. Zero
is neither a fraction nor a decimal, so zero is an whole
number.

12. integers
 Integers are the number which include positive and
negative numbers.
 Negative numbers are the numbers that are less than
zero. They are the opposite of positive numbers.
Negative numbers are usually written with a negative
sign (also called a minus sign) in front of the number
they are opposite of. When the set of negative
numbers is combined with the natural numbers zero,
the result is the set of integer numbers also called ‘Z’.

13. Rational numbers
 A rational number is a number that can be expressed
as a fraction with integer numerator and a non zero
natural number denominator. The symbol of the
rational number is ‘Q’.
 It includes all types of numbers other than irrational
numbers, i.e it includes integers, whole numbers,
natural numbers etc…

14. fractions
 This is a type of rational number. Fractions are written
as two numbers, the numerator and the denominator,
with dividing bar between them.
 In the fraction m/n ‘m’ represents equal parts, where
‘n’ equal parts of that size make up one whole.
 If the absolute value of ‘m’ is greater than ‘n’ ,then the
absolute value of the fraction is greater than1. fractions
can be greater than, less than, or equal to 1 and can
also be positive, negative, or zero.

15. Irrational numbers
 If a real number cannot be written as a fraction of two
integers i.e it is not rational, it is called irrational
numbers. A decimal that can be written as a fraction
either ends (terminates) or forever repeats about.
 Real number (PI) is an example of irrational number.
PI value is-3.141593653……… the number neither start
repeating themselves nor come in specific pattern.

16. Decimal expansion of
numbers
 A decimal expansion of a number can be either:-
 Terminating
 Non terminating, non reccuring
 Non terminating, reccuring

17. 1. terminating
 A decimal expansion in which the remainder becomes
zero. For example- 64 is divided by 8, the remainder
becomes zero . As the remainder is zero ,this is a
terminating decimal.
 Terminating decimal is always a rational number. It
can be written in the form p/q form.

18. 2.NON TERMINATING,
NON RECURRING
 ‘recurring’ means ‘repeating’. In this form, when we
divide a number by another, remainder never becomes
zero and also the number does not repeat themselves
in a specific pattern. If a number is non terminating
and non repeating, they are always classified as
irrational number.
 For example: 0.001000100400026……… does have a
pattern, but it is not a fixed length recurring pattern.
So the number is irrational.

19. 3.non terminating,
recurring
 In this form, when a number is divided by the other,
instead the number of the quotient start repeating
themselves, such numbers are classified as non
terminating, recurring.
 For example-3.624624624……….
 In this example, ‘624’ have started repeating itself.
Hence, it is a rational number. It can be expressed in
p/q form.

20. Number line
 A number line is a line with the marks on it that are
placed at equal distance apart. One mark on the
number line is usually labelled zero and then each
successive mark to the left or to the right of the zero
represent a particular unit such as 1,or 0.5. It is a
picture of a straight line.

21. SUCCESSIVE MAGNIFICATION
 On the number line, there are infinite smaller
numbers lying between any two numbers. These
smaller numbers can be of two, three or more decimal
places. To see or mark such numbers clearly. We use
the process called successive magnification of the
number line. Here, we use a virtual(imaginary)
magnifying glass to enlarge the smaller divisions on
number line.
 This procedure can be used to visualise a real number
with a non terminating, non recurring decimal
expansion on the number line.

22. rationalization
In elementary algebra, root rationalization is a process
by which surds in the denominator of an irrational
fraction are eliminated.
These surds may be monomial or binomials involving
square roots, in simple examples. There are wide
extension to the technique.

23. Rationalizing factor
It is difficult to deal with the expression having square
root in the denominator. This raise a need of removing
square root from the denominator. It can be done by
rationalizing the denominator.