Number Systems – A Brief Overview
The basics for mathematics begin with the study of Number Systems for every class. It is included as the first very chapter so that you can get familiar with the various kinds of numbers which are possible and known to us. They are used to deal with various concepts of mathematics.
Therefore, getting acquainted with international number system becomes a necessity for you to ace in Mathematics. In this pursuit, having quality notes by your side can aid to your experience, and you will be able to progress in this chapter with ease.
Introduction to Number System
There can be several kinds of numbers as per the mathematical Number System definition. The various kinds of numbers are ass discussed below –
Natural Numbers – It is represented by ‘N’ and all positive numbers starting from 1 to infinity are known as natural numbers. For example, 1, 2, 3, 4, 5, . . . . . . and so on.
Whole Numbers – It is represented by ‘W’, and all the natural numbers starting from ‘0’ makes into this list. It is to note that whole numbers do not comprise of negative numbers, fractions, or decimals, etc. For example, 0, 1, 2, 3, 4, 5, . . . . . . and so on.
Integers – All whole numbers, in addition to the negative numbers, make integers. For example, 0, 1, 2, -3, -5. Etc.
Real Numbers – A real number is said to be one which can be represented in the number line and is represented by ‘R’. The number line has in-numerous points, and each one represents a unique real number. It can also include rational or irrational numbers.
Rational Numbers – The numbers which are represented in p/q form are known as rational numbers. Here, q and p both are integers, and the value of q is never equal to zero.
Irrational Numbers – Those numbers which are not in the p/q form where the value of q is zero are in the list of irrational numbers. For instance, 1.010024563…, π, e, √2, etc. are examples of an irrational number.
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Representation of Real Numbers on Number Line
As from the information about number system, the successive magnification process is used to represent real numbers on number line. For example, consider this question.
Mark 4. \[\overline{26}\] on the number line up to 4 decimal places.
You can mark it on the number line using the steps mentioned as follows.
Step 1. Since the given number 4.26 is in between 4 and 5, divide the number line into ten equal parts beginning from 4 till 5.
Step 2. Since the given number 4.26 is in between 4.2 and 4.3, divide the number line into ten equal parts beginning from 4.20 till 4..30.
Step 3. Following the same process, divide it further into ten equal parts starting from 4.260 and ending at 4.270.
Step 4. Follow the same process again and, divide it further into ten equal parts starting from 4.2620 and ending at 4.263.
Here, look at the picture to get a clearer idea about the steps.
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Now that you are aware and have learnt the concept of Number System in Mathematics, you will be able to improve your knowledge. In case you are inquisitive and want to dig deep in the mathematical concepts, Vedantu can help you with that.
You can refer to our Number System examples with solutions prepared by qualified tutors and prepare better for exams. Download our Vedantu app to learn more on the go.
FAQs on Number Systems
1. What is the importance of number system in maths?
Ans. The number system meaning comprises of all kinds of numbers which is possible and permissible within the boundaries of mathematics and is known to humankind through experimentation and derivation. The various numbers form the basics of mathematics, and all calculations can be made based on these numbers only. The different types of number system help mathematician derive various formulas and find answers to various concepts which are still unknown to the world. The finding of various numbers in number systems has contributed a lot in the study and research of mathematics as a subject.
2. What is the Indian numbering system?
Ans. In the Indian number system in maths, the digits from 0 to 9 are used for writing all numbers where ‘0’ is termed as an insignificant digit and others are known as a significant digit. It follows an initial 3-digit split and then the numbers are followed by a 2-digit split. For example, here look at the numbers to understand the splits. 1,000 indicate the 3-digit split. 10,000 denote the 2-digit split which follows the initial three-digit split. Thereafter, the 2-digit split continues and is shown by the following numbers 1,00,000, 5,23,457, or 11, 23, 45, 967.
3. How is Indian system different from international numerical system?
Ans. The international number systems also use the same digits to write numbers and are almost the same as the Indian number systems. The major difference between the international system and Indian system is the way they use commas and separators. For instance, after thousands place, a comma is used for lakh. However, in case of the international system, a comma is used after a million. For example, there is a 2-digit split after the initial split of 3-digit in Indian standard as 1,00,000. In international standard, the three-digit split continues in all cases. This can be quickly shown by the following numbers 2,000, 5,000,000, 1,000,000,000, etc.
4. Is it beneficial to read NCERT solutions for Class 9 Maths chapter 1 Number System?
Ans. It is essential to grasp the concept of number system to build a fundamental knowledge base that can help you learn mathematics quickly and excel in it. While the chapter may seem to be a bit complicated at first, you will be able to understand the basic concepts correctly with a solution to guide you. Get help from the solution and learn the definition of decimal number system and other related concepts. This will help you perform well in the academics as you will not face trouble solving even the complicated questions.
