NCERT Solutions Class 9 Chapter 1 Number System Ex 1.1

Exercise 1.1 is the starting point of the Number System Class 9 chapter, and it builds the base for everything you learn ahead. This exercise introduces different types of numbers such as natural numbers, whole numbers, integers, and rational numbers. The solutions for Number System Class 9 Exercise 1.1 are written in simple steps so students can understand the concepts without confusion. 

Number System Class 9 Exercise 1.1 Solution

Class 9 Chapter 1 Number System Exercise 1.1 NCERT solutions help you solve every question confidently. Questions as well as the answers are given here for better preparation: 

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

Solution: We know that a number is said to be rational if it can be written in the form p/q, where p and q are integers and q ≠ 0. Taking the case of ‘0’, Zero can be written in the form 0/1, 0/2, 0/3 … as well as, 0/1, 0/2, 0/3 .. Since it satisfies the necessary condition, we can conclude that 0 can be written in the p/q form, where q can either be a positive or negative number. Hence, 0 is a rational number.

2. Find six rational numbers between 3 and 4.

Solution: There are infinite rational numbers between 3 and 4. As we have to find 6 rational numbers between 3 and 4, we will multiply both the numbers, 3 and 4, with 6+1 = 7 (or any number greater than 6)

i.e., 3 × (7/7) = 21/7 and, 4 × (7/7) = 28/7. The numbers in between 21/7 and 28/7 will be rational and will fall between 3 and 4. Hence, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7 are the 6 rational numbers between 3 and 4.

3. Find five rational numbers between 3/5 and 4/5.

Solution: There are infinite rational numbers between 3/5 and 4/5. To find out 5 rational numbers between 3/5 and 4/5, we will multiply both the numbers

3/5 and 4/5 with 5+1=6 (or any number greater than 5)

i.e., (3/5) × (6/6) = 18/30 and, (4/5) × (6/6) = 24/30

The numbers in between18/30 and 24/30 will be rational and will fall between 3/5 and 4/5. Hence,19/30, 20/30, 21/30, 22/30, 23/30 are the 5 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.

Solution: True

Natural numbers- Numbers starting from 1 to infinity (without fractions or decimals) i.e., Natural numbers = 1,2,3,4…

Whole numbers – Numbers starting from 0 to infinity (without fractions or decimals) i.e., Whole numbers = 0,1,2,3… Or, we can say that whole numbers have all the elements of natural numbers and zero. Every natural number is a whole number; however, every whole number is not a natural number.

(ii) Every integer is a whole number.

Solution: False

Integers- Integers are set of numbers that contain positive, negative and 0; excluding fractional and decimal numbers. i.e., integers= {…-4,-3,-2,-1,0,1,2,3,4…}

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals) i.e., Whole numbers= 0,1,2,3…. Hence, we can say that integers include whole numbers as well as negative numbers. Every whole number is an integer; however, every integer is not a whole number.

(iii) Every rational number is a whole number.

Solution: False

Rational numbers- All numbers in the form p/q, where p and q are integers and q≠0. i.e., Rational numbers = 0, 19/30 , 2, 9/-3, -12/7…

Whole numbers- Numbers starting from 0 to infinity (without fractions or decimals) i.e., Whole numbers= 0,1,2,3…. Hence, we can say that integers include whole numbers as well as negative numbers. All whole numbers are rational, however, all rational numbers are not whole numbers.

NCERT Maths Class 9 Number System Exercise 1.1 PDF

The PDF for Number System Class 9 Exercise 1.1 gives you access to solved answers anytime. It is useful for practice, last-minute preparation, and practising questions step-by-step. Students preparing for tests or struggling with basics can use this PDF to improve speed and accuracy.

NCERT Maths Class 9 Number System Exercise 1.1 PDF

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