Class-9 Subject-Maths Chapter-1 Slot-1 Number Systems( Exercise 1.3)

 EVENTS CONVENT HIGH SCHOOL
10/08/2021          CLASS-9         SESSION2021-22(SLOT-1)
Maths
Chapter-1 Number Systems
EXERCISE 1.3
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Class-9 Subject-Maths Chapter-1 Exercise1.2 (NUMBER SYSTEM)

 

EVENTS CONVENT HIGH SCHOOL
05/08/2021          CLASS-9         SESSION2021-22(SLOT-1)
Maths
Chapter-1 EXERCISE 1.2
NUMBER SYSTEM
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 Question 1.State whether the following statements are true or false. Justify your answers.

(i) Every irrational number is a real number.
(i) True-Because all rational numbers and all irrational numbers form the group (collection) of real numbers.

 (ii) Every point on the number line is of the form √m , where m is a natural number.

(ii) False-Because negative numbers cannot be the square root of any natural number.

 (iii) Every real number is an irrational number.

 (iii) False-Because rational numbers are also a part of real numbers.

 

Question 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.

Solution:No, if we take a positive integer, say 9, its square root is 3, which is a rational number.

 

Question 3.Show how √5 can be represented on the number line.

Solution:Draw a number line and take point O and A on it such that OA = 1 unit. Draw BA ⊥ OA as BA = 1 unit. Join OB = √2 units.

Now draw BB1 ⊥ OB such that BB1 =1 unit. Join OB1 = √3 units.

Next, draw B1B2⊥ OB1such that B1B2 = 1 unit.

Join OB2 = units.

Again draw B2B3 ⊥OB2 such that B2B3 = 1 unit.

Join OB3 = √5 units.

Take O as centre and OB3 as radius, draw an arc which cuts the number line at D.

Point D

represents √5 on the number line.

 

Class-9 Subject-Maths Chapter-1 Slot-1 Number Systems

 

EVENTS CONVENT HIGH SCHOOL
31/07/2021          CLASS-9         SESSION2021-22(SLOT-1)
Maths
Chapter-1
NUMBER SYSTEM(Ex.1.1)
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Exercise 1.1 Explain

    
Question 1.Is zero a rational number? Can you write it in the form pq,where p and q are integers and q ≠0?

Solution:Yes, zero is a rational number it can be written in the form pq.

0 = 01 = 02 = 03 etc. denominator q can also be taken as negative integer.

 

Question 2.Find six rational numbers between 3 and 4.

Solution:Let qi be the rational number between 3

and 4, where j = 1 to 6.

∴ Six rational numbers are as follows:

Thus, the six rational numbers between 3 and 4 are

Question 3.Find five rational numbers between 35 and 45.

Solution:Since, we need to find five rational numbers, therefore, multiply numerator and denominator by 6.

Question 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.

Solution:

(i) True

∵ The collection of all natural numbers and 0 is called whole numbers.

(ii) False

∵ Negative integers are not whole numbers.

(iii) False

∵ Rational numbers are of the form p/q, q ≠ 0 and q does not divide p completely that are not whole numbers.