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NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)

Q1. Is zero a rational number? Can you write it in the form p/q where p and q are integers and q ≠ 0?
Ans: 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

Taking the case of '0',

Yes, zero is a rational number.
0 =NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)
Example : NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)

Since, it satisfies the necessary condition, we can conclude that 0 can be written in the p/q form, where q can either be positive or negative number.
Hence, 0 is a rational number.


Q2. Find six rational numbers between 3 and 4.
Ans: We can find any number of rational numbers between two rational numbers. There are infinite rational numbers between 3 and 4.

  • First of all, we make the denominators same by multiplying or dividing the given rational numbers by a suitable number. 
  • If denominator is already same then depending on number of rational numbers we need to find in question, we add one and multiply the result by numerator and denominator.

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)

NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)

We can choose 6 rational numbers as: NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)andNCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)


Q3. Find five rational numbers between 3/4 and 4/5.
Ans: There are infinite rational numbers between 3/4 and 4/5.

Since we need to make the denominators same first, then
NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)

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)

NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)
∴ Five rational numbers between NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)areNCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)andNCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)


Q4. State whether the following statements are true or false. Give reasons for your answers.
(i) Every natural number is a whole number.
Ans: True
Natural Numbers: Natural numbers are set of numbers that contain numbers from 1 to infinity.  Set of natural numbers is represented as N= {1, 2, 3…….}.
Whole numbers: Numbers starting from 0 to infinity (without fractions or decimals)
Set of  Whole numbers  is represented as W= 0,1,2,3….
As all the natural numbers comes in the set of whole numbers. Hence, every natural number is a whole number.

(ii) Every integer is a whole number.
Ans: 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.
Ans: 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.
Every whole number is rational, however, every rational number is not a whole number.

The document NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1) is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on NCERT Solutions for Class 9 Maths Chapter 1 - Number System (Exercise 1.1)

1. What is the number system and why is it important in mathematics?
Ans. The number system is a way of categorizing numbers based on their properties. It includes natural numbers, whole numbers, integers, rational numbers, and irrational numbers. Understanding the number system is essential in mathematics because it forms the foundation for various mathematical concepts, operations, and real-world applications.
2. What are the different types of numbers in the number system?
Ans. The number system comprises several types of numbers: 1. Natural Numbers: Counting numbers starting from 1 (1, 2, 3, ...). 2. Whole Numbers: Natural numbers including 0 (0, 1, 2, 3, ...). 3. Integers: Whole numbers and their negative counterparts (..., -3, -2, -1, 0, 1, 2, 3, ...). 4. Rational Numbers: Numbers that can be expressed as a fraction (p/q), where p and q are integers and q ≠ 0. 5. Irrational Numbers: Numbers that cannot be expressed as a fraction, such as √2 or π.
3. How do you represent rational numbers on a number line?
Ans. To represent rational numbers on a number line, first identify the whole numbers around the rational number. Then, divide the space between these whole numbers into equal parts based on the denominator of the rational number's fraction. For example, to represent 3/4, locate 0 and 1 on the number line, divide the segment into four equal parts, and count three parts from 0 to mark 3/4.
4. Can you give examples of rational and irrational numbers?
Ans. Yes! Examples of rational numbers include 1/2, -3, and 0.75, as they can be expressed as fractions. Examples of irrational numbers include √3, π, and e, which cannot be represented as fractions of integers.
5. What is the significance of understanding the properties of numbers in the number system?
Ans. Understanding the properties of numbers in the number system is significant because it helps in performing operations accurately, solving mathematical problems, and comprehending advanced topics in mathematics. It also aids in logical reasoning and problem-solving skills, which are essential in everyday life and various fields of study.
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