NCERT Class 9 Maths Chapter 1 Number Systems Exercise 1.1 Solutions | Step-by-Step Explanation
Chapter: Number Systems
Class: 9 (CBSE)
Exercise: 1.1
Introduction
In this article, we provide complete step-by-step solutions for NCERT Class 9 Maths Chapter 1 – Number Systems Exercise 1.1. Each solution is explained with proper concepts and formulas to help students understand the fundamentals clearly.
Important Concepts Used in Exercise 1.1
1. Rational Number
A number is called a rational number if it can be written in the form:
p/q, where p and q are integers and q ≠ 0.
2. Natural Numbers
1, 2, 3, 4, 5, …
3. Whole Numbers
0, 1, 2, 3, 4, 5, …
4. Integers
…, -3, -2, -1, 0, 1, 2, 3, …
Exercise 1.1 Solutions
Question 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 rational number can be written in the form:
p/q (where q ≠ 0)
Now consider zero:
0 = 0/1
Here:
p = 0 (integer)
q = 1 (integer and not equal to 0)
Since it satisfies the definition of a rational number,
Final Answer: Yes, zero is a rational number.
Question 2
Find six rational numbers between 3 and 4.
Solution:
Convert the integers into fractions with the same denominator:
3 = 30/10
4 = 40/10
Now choose six numbers between 30 and 40:
31/10, 32/10, 33/10, 34/10, 35/10, 36/10
These are equivalent to:
3.1, 3.2, 3.3, 3.4, 3.5, 3.6
Final Answer: Six rational numbers between 3 and 4 are:
31/10, 32/10, 33/10, 34/10, 35/10, 36/10
Question 3
Find five rational numbers between 3/5 and 4/5.
Solution:
Make denominators larger by multiplying both fractions by 10:
3/5 = 30/50
4/5 = 40/50
Now select five numbers between 30 and 40:
31/50, 32/50, 33/50, 34/50, 35/50
Final Answer: Five rational numbers between 3/5 and 4/5 are:
31/50, 32/50, 33/50, 34/50, 35/50
Question 4
State whether the following statements are true or false. Give reasons.
(i) Every natural number is a whole number.
Natural Numbers: 1, 2, 3, 4, …
Whole Numbers: 0, 1, 2, 3, 4, …
All natural numbers are included in whole numbers.
Answer: True
(ii) Every integer is a whole number.
Integers include negative numbers such as -1, -2, -3.
Whole numbers do not include negative numbers.
Answer: False
Reason: Negative integers are not whole numbers.
(iii) Every rational number is a whole number.
Example: 1/2 is a rational number but not a whole number.
Answer: False
Reason: Many rational numbers are not whole numbers.
Conclusion
In Exercise 1.1, students learn:
- Definition of rational numbers
- How to find rational numbers between two numbers
- Difference between natural numbers, whole numbers, and integers
- Logical reasoning in number classification
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