1.Number System

Class IX(Chapter 1.Numbers System)

1.Natural Number (N) : All number s  used in counting are known as natural numbers such  as

1,2,3,….., is called natural number.Denoted by N.N={1,2,3,……,n}.

2.Whole Number(W): All natural numbers including zero , is called Whole numbers.Denoted by W.


3.Integers(I):- All number with +ve and –ve sign including 0, is known as Integers.Denoted by I.


4. Rational number(Z):-A number ‘r’ is called a rational number, if it can be written in the form p/q,where p and q are integers and q ¹ 0. Such as 2/5,/9 etc

 Fact 1:-Pythagoras  discovered irrational numbers around 400 BC. These numbers are called irrational numbers(irrationals), because they cannot be written in the form ofa ratio of integers.

Fact2:- Hippacus has an unfortunate end, either for discovering that 2 is irrational

Fact 3:- Historical Fact  Z comes from theGerman word “zahlen”, which means“to count”

Fact4: The Greek genius Archimedes was the first to compute digits in the decimal expansion of p. He showed 3.140845< p < 3.142857. Aryabhatta (476 – 550 C.E.), the great Indian mathematician and astronomer, found the value of p correct to four decimal places (3.1416).

Example: Find five rational numbers between 1 and 2.

Solution: Since we want five numbers, we write 1 and 2 as rational numbers with denominator 5 + 1,

i.e., 1 =6/6 and 2 =12/6

. Then We can check that 7/6,8/6,9/6,10/6 and 11/6 are all rational

numbers between 1 and 2. So, the five numbers are 7/6,8/6,9/6,10/6 and 11/6.

5. Irrational number :-A number ‘s’ is called irrational, if it cannot be written in the form p/q

, where pand q are integers and q ¹ 0. Example:- 2, 3, 15,, p, 0.10110111011110…

6.Real numbers(R):- the collectionof all rational numbers and irrational numbers together

make up what we call the collection of real numbers,

which is denoted by R. Therefore, a real number is either rational or irrational.

 We can say that every real number is represented by a unique point on the number

line. Also, every point on the number line represents a unique real number.This is why we call the number line, the real number line.

Leave a Reply

Your email address will not be published. Required fields are marked *

You have successfully subscribed to the newsletter

There was an error while trying to send your request. Please try again.

EduInfoshare will use the information you provide on this form to be in touch with you and to provide updates and marketing.