The study of numbers forms 2023 NCERT Math Class 9 Number System, and a solid understanding of the number system is crucial for students’ mathematical development. In this comprehensive blog post, we will delve into the intriguing world of the number system as taught in Class 9 Mathematics. From the basic building blocks of natural numbers to the vast realm of real numbers, we will explore concepts such as number lines, rational numbers, irrational numbers, whole numbers, integers, and more. So, let’s embark on this mathematical journey together!
2023 NCERT Math Class 9 Number System : Natural Numbers:
The number system begins with the set of natural numbers. Natural numbers, denoted as N, comprise the counting numbers: 1, 2, 3, 4, and so on. These numbers represent quantities used for counting, such as the number of objects or people.
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2023 NCERT Math Class 9 Number System : Whole Numbers:
Expanding upon the natural numbers, the set of whole numbers, denoted as W, includes zero (0) along with the counting numbers. Whole numbers allow us to represent the absence of objects or null quantities. In essence, whole numbers form a more comprehensive representation of quantities.
2023 NCERT Math Class 9 Number System : Integers:
Integers, denoted as Z, encompass both positive and negative numbers along with zero. Integers allow us to represent values in the opposite direction on a number line. For every positive number, there exists a corresponding negative number, forming a symmetrical representation.
2023 NCERT Math Class 9 Number System : Rational Numbers:
Rational numbers, denoted as Q, encompass numbers that can be expressed as a fraction of two integers, where the denominator is not zero. Rational numbers include both terminating and repeating decimals. They can be positive, negative, or zero. For example, 1/2, -3/5, 2/7 are all rational numbers.
2023 NCERT Math Class 9 Number System : Irrational Numbers:
Irrational numbers, denoted as I, are numbers that cannot be expressed as fractions and do not terminate or repeat as decimals. They possess an infinite and non-repeating decimal representation. Examples of irrational numbers include √2, π (pi), and e (Euler’s number). The decimal expansion of irrational numbers is non-terminating and non-repeating.
2023 NCERT Math Class 9 Number System : Real Numbers:
The set of real numbers, denoted as R, encompasses both rational and irrational numbers. It includes all possible numbers on the number line, from negative infinity to positive infinity. Real numbers consist of integers, fractions, terminating decimals, and infinite non-repeating decimals.
2023 NCERT Math Class 9 Number System : Number Line:
A number line is a visual representation of the entire number system. It helps us visualize the relative positions and relationships between different types of numbers. On a number line, natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers are placed at appropriate positions.
NCERT Class 9 Math 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?
A1. Yes, zero is indeed a rational number. It can be expressed in the form of p/q, where both p and q are integers, and q is not equal to zero.
To represent zero in this form, we can choose any value of p as zero and any non-zero value of q. For example, we can write 0 as 0/1 or 0/2 or 0/1000, and so on. In each case, p is zero, and q is a non-zero integer, satisfying the condition for a number to be rational.
The fact that any integer divided by non-zero integer results in a rational number, including the division of zero by a non-zero integer, reinforces the classification of zero as a rational number.
Q2. Find six rational numbers between 3 and 4
A2. There are infinite rational numbers between 3 and 4. (6+2=8) We need to find 6 rational numbers so we will multiply numerator and denominator with 8. This can be represented as 24/8 and 32/8(multiplying both 3/1 and 4/1 by 8/8) respectively, therefore 6 rational numbers between 3 and 4 are 25/8 ,26/8 ,27/8 ,28/8 ,29/8 ,30/8.
Q3. Find five rational numbers between 3/5 and 4/5
A3.There are infinite rational numbers between 3/5 and 4/5. (5+1=6) We need to find 5 rational numbers so we will multiply numerator and denominator with 6. This can be represented as 18/30 and 24/30(multiplying both 3/5 and 4/5 by 6/6)respectively,therefore 5 rational numbers between 3/5 and 4/5 are 19/30 ,20/30 ,21/30 ,22/30 ,23/30
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.
A3.(i) True,since the collection of whole numbers contain all the natural numbers.
(ii) False,as integers maybe negative but whole numbers are always positive for example -5 is a integer but not a whole number.
(iii)False,as rational can be fractional but whole number cannot be fractional for example,2/3 is a rational number but not a whole number.
Conclusion:
The study of the number system in Class 9 Mathematics is a foundational step towards understanding and utilizing numbers in various mathematical contexts. From the basic concept of natural numbers to the intricate properties of irrational numbers and real numbers, each component plays a vital role in our mathematical journey.
By grasping the concepts of number lines, rational numbers, irrational numbers, whole numbers, integers, and real numbers, students can develop a deeper understanding of mathematical operations, equations, and problem-solving strategies.
Embrace the beauty and intricacy of the number system, as it provides a framework for exploring and understanding the mathematical universe. So, let’s continue to explore, discover, and apply the concepts of the number system to expand our mathematical horizons!
