Easy Number System (Class 9th Maths-NCERT-Chapter-1)

Introduction to Number system:

In Number system, Numbers that can be represented on number line are called real numbers. Real Numbers are the combination of Rational and Irrational numbers. Real numbers can be classified as Natural Numbers, Whole Numbers, Integers etc.

-By Mohammad Al Saif

We will discuss about Natural Numbers, Whole Numbers, Integers, Rational and Irrational Numbers in this number system article.

---

1. Natural Numbers (Counting Numbers) :

1,2,3,4,5,6… Natural Numbers are denoted by ‘N’.

---

2. Whole Numbers :–

0,1,2,3,4,5…
Whole Numbers are denoted by ‘W’.
Note:- All Natural Numbers are Whole Numbers but all Whole Numbers are not Natural Numbers. (Because 0 is a whole number but not a natural number)

---

3. Integers in Number System:-

..-3,-2,-1,0,1,2,3,…
Integers are denoted by ‘Z’.
Positive Integers :- 1,2,3…
Negative Integers :- -1,-2,-3, ..
Zero Integer :- 0 (Neither Positive Nor Negative)

For More:- You can check out the above video and you can also check out “EduTalk With Saif YouTube Channel” to learn Class 9th Mathematics and Maths Basics.

---

4. Rational Numbers in Number System :-

Numbers which can be expressed in the form of ratio of two numbers i.e p/q where p & q are integers and q ≠ 0 (because division by zero is not defined. Why?) Rational Numbers are either Terminating Decimals or Non-Terminating and Recurring (Repeating) Decimals.

e.g. Terminating Decimals : 5/2 = 2.5,

Non Terminating and Recurring Decimals : 10/3 = 3.3333…

NOTE:-0 is a Rational number because we can write 0 as 0/1 or 0/2 or 0/3… where p=0 and q may be 1,2,3…

Example : Are the following statements true or false? Give reasons for your answers.
(i) Every whole number is a natural number.
(ii) Every integer is a rational number.
(iii) Every rational number is an integer.

Answer:

(i) False, because zero is a whole number but not a natural number.
(ii) True, because every integer m can be expressed in the form m/1, and so it is a rational number.
(iii) False, because 3/5 is not an integer.

Exercise 1.1 (source: NCERT)

1. Is zero a rational number? Can you write it in the form p/q, where p and q are integers
   and q not is not equal to 0?
2. Find six rational numbers between 3 and 4.
3. Find five rational numbers between 3/5 and 4/5.
4. State whether the following statements are true or false. Give reasons for your answers.
   (i) Every natural number is a whole number.
   (ii) Every integer is a whole number.
   (iii) Every rational number is a whole number.

watch video if needed for the solution.(RECOMMENDED: try yourself first)

---

5. Irrational Numbers :-

Numbers which can’t be represented in the form p/q where p & q are integers and q ≠ 0 . Irrational Numbers are Non-Terminating Non Repeating Decimals. Also, square root of numbers not having perfect square root are irrational numbers.

e.g. Non-Terminating Non-Repeating : 1.01001000100001… , π (pi) , 1.12122122212222…

Square root of numbers not having perfect square root : √2, √3, √5, √7, √8, √10 etc.

Remark : Did you Remember that when we use the symbol √ ( called under root), we assume that it is the
positive square root of the number. So √ 4 = 2, though both 2 and –2 are square
roots of 4.

Exercise 1.2 (source: NCERT)

1. State whether the following statements are true or false. Justify your answers.
   (i) Every irrational number is a real number.
   (ii) Every point on the number line is of the form root(m) , where m is a natural number.
   (iii) Every real number is an irrational number.
2. Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.
3. Show how 5 can be represented on the number line.

watch video if needed for the solution.(but RECOMMENDED: try yourself first)