S.no Title Pg.no

1. Acknowledgement 3

2. Number system 4

3. What is number system? 5

4. Parts of number system 6

5. Explanation 7-11

6. Simple positive numbers 12-13

7. Summary 14-16

8.

I would like to express my special thanks of gratitude to my teacher Mrs. Pooja Kaushal as well as our principal Mrs. Malik who gave me the golden opportunity to do this wonderful project on the topic Number Systems which also helped me in doing a lot of Research and i came to know about so many new things I am really thankful to them.Secondly, i would also like to thank my parents and friends who helped me a lot in finalizing this project within the limited time frame.

ACKNOWLEDGEMENT

WHAT IS NUMBER SYSTEM ?A numeral system (or system of

numeration) is a writing system for expressing numbers, that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

Number SystemNatural Numbers

Whole Number

Integers

Rational Numbers

Irrational Numbers

(N )

W

Z

Q

I

NATURAL NUMBERS

The Natural Numbers are those used for counting.

Properties of the natural numbers related to divisibility.

There is no universal agreement about whether to include zero in the set of natural numbers.

WHOLE NUMBER

Whole numbers are easy to remember.

The only thing that makes them different than natural numbers is that we include the zero

Whole numbers are 1, 2, 3, 4, and mire

RATIONAL NUMBERSRational numbers have integers AND fractions AND decimals.

Now you can see that numbers can belong to more than one classification group. Rational numbers can also have repeating decimals

INTEGERSIntegers can be whole numbers or they can be whole numbers.

Whole numbers with a negative signs in front of them.

Individuals often refer to integers as the positive and negative numbers.

IRRATIONAL NUMBERS

However, irrational numbers can have a decimal value that continues forever WITHOUT a pattern

Irrational numbers don't include integers OR fractions.

An example of a well known irrational number is pi which as we all know is 3.14 but if we look deeper at it, it is actually 3.14159265358979323846264338327950288419.....and this goes on for somewhere around 5 trillion digits!

SIMPLEPOSITIVE

NUMBERS

A Number r is called a rational number , if it can be written in the form p/q where p & q are integers & q is not = o.

A number s is called a irrational number, if it cannot be written in the form p/q , where p & q are integers & q is not = o.

The decimal expansion of a rational number is either terminatingor non-terminating recurring. Moreover ,a number whose decimal expansion is terminating or non-terminating recurring is rational.

The decimal expansion of an irrational number is non-terminating non- recurring . Moreover, a number whose decimal expansion is

non –terminating non – recurring is irrational.

All the rational and irrational numbers make up the collection of real numbers.

THE NCERT COURSE BOOK OF IX CLASSTH

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There is a unique real number corresponding to every point on the number lineAlso, corresponding to each real number, there is a unique point on the

number line

If r is rational and s is irrational ,then r +s & r-s are irrational numbers, and rs and r/s are irrational numbers, r is not = 0

For positive real numbers a and b, the following identities hold :

√ab=√a√b √a/b=√a/√b

(√a+√b ) (√a-√b)=a-b

(a+√b) (a-√b)=a-b

(√a+√b) = a+ 2√ab+b

From,AKHIL PRASADAMAN KUMARTILAK LANKA

NAVEEN KUMARRAHUL KUMAR

SUCHIN&

ABHISHEK SINGH