Essential Number System Formulas for CBSE 9th Maths Success
Do you find it difficult to cope up with the Math formulas and equations? Do math formulas seem to be complicated to remember? Not a matter to distress over. What if we tell you that you no longer require struggling to mug up all Math formulas of Class 9? Yes! You will get formulas of the number system in the Class 9 Maths Formula Sheets designed by subject matter experts at Vedantu. This sheet is inclusive of all formulas of number system class 9 chapters wise.
Where can I find Formulas of Maths of Class 9?
CBSE Class 9 Maths Formulas all chapters are available for free access and revision on Vedantu.com. You can simply download the important Maths Formulas and equations PDF 9th class to solve the problems easily, quickly and score higher grades in your Class 9 CBSE Board Exams at Vedantu.
Number System Class 9
Natural Numbers: These are in numerical form of -1, 2, 3, 4, 5, 6, 7, 8, 9, 10..........denoted by N.
Whole Numbers: These are in numerical form of – 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10..........denoted by W.
Integers: -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 denoted by Z.
Rational Numbers: All the numbers that can be mathematically written in the form p/q, q ≠0 are known as rational numbers where p and q refers to the integers.
Irrational Numbers: A number‘s’ is known as irrational, if it cannot be mathematically written in the form p/q where p and q are integers and q ≠ 0.
Decimal Expansion: Such an algebraic expansion in the decimal form of a rational number is either terminating or non terminating recurring. Therefore, we can say that a number whose decimal expansion is either terminating or non terminating/ recurring is what we call a rational number. There are following properties of a decimal expansion which are as below:
For an irrational number, the decimal expansion is non terminating and non recurring.
All the rational numbers and irrational numbers can be taken together.
We can make a collection of real numbers.
A real number may be either rational or irrational.
If ‘r’ is rational and ‘s’ is irrational then r + s, r - s, r . s will invariably be the irrational numbers, however r/s may either be rational or irrational
We can represent every irrational number on a number line using Pythagoras theorem.
Rationalization is the method of taking out square roots from the denominator. For example, for a mathematical expression 2 + √6/√4, to remove we will multiply both numerator as well as denominator by √4.
Important Number System Formula Class 9
1. Polynomial Expressions Formulas
2. Coordinate Geometry Formulas
3. Circles Formulas
How to Learn all the Formulas of CBSE Class 9 Maths Number Systems?
Number systems comprise a variety of formulas such as the circumference of a circle, polynomial expressions, distance formula, etc. If you do not learn all the formulas properly, you can get confused and will not be able to solve the question. Here are some tips on how to learn all the formulas of CBSE Class 9 Maths Number Systems:
When you are learning any formula of CBSE Class 9 Maths Number Systems, you should go through its definitions and explanations given in the textbook to understand what the formula is about.
After learning a formula, you should use the solved examples in textbooks and reference books to understand how to apply it and solve a question correctly.
CBSE Class 9 Maths Number Systems Formulas - Number System, Important Number System Formula, and FAQs available on Vedantu provide you with explanations in simple language. You can use our platform to revise these formulas and improve your understanding of Number Systems.
Once you have learned all the formulas, try solving questions based on CBSE Class 9 Maths Number Systems. By practising these questions, you can learn how to use a formula in a question and improve your mathematical skills.
While learning the formulas of CBSE Class 9 Maths Number Systems Formulas, you should also learn how they were derived. By learning the derivation of a formula, you can understand the concept more clearly.
Why is Number Systems Important for CBSE Class 9 Maths Students?
Maths is an important subject for CBSE Class 9 students. The CBSE Class 9 Maths syllabus comprises a lot of important concepts that are necessary to learn. Number systems are one of these concepts. Learning the number systems is really helpful as it makes other concepts of Class 9 Maths easier to understand.
Below are some other reasons why you should learn number systems:
The CBSE Class 9 Maths Number Systems Formulas - Number System, Important Number System Formula, and FAQs give you a better understanding of real numbers, integers, natural numbers, and whole numbers.
Learning about CBSE Class 9 Maths Number Systems will help you learn other concepts in your maths syllabus with ease.
Number systems contain many formulas, including polynomial functions, circles, and geometry. So, learning the CBSE Class 9 Maths Number Systems will assist you in solving questions based on these topics too.
The CBSE Class 9 Maths Number Systems carry a significant amount of weightage in the Class 9 Maths exam. If you go through this concept thoroughly, you will be able to score well in the exam.
FAQs on CBSE Class 9 Number Systems: All Formulas Explained
1. What are the formulas of number system class 9?
The number system formulas for CBSE Class 9 include fundamental expressions and properties that underpin the study of rational and irrational numbers, real numbers, and their representation. Key formulas are:
- Closure property: For any two real numbers $a$ and $b$, $a + b$ and $a \times b$ are real numbers.
- Commutative property: $a + b = b + a$ and $a \times b = b \times a$
- Associative property: $(a + b) + c = a + (b + c)$; $(a \times b) \times c = a \times (b \times c)$
- Distributive property: $a \times (b + c) = a \times b + a \times c$
- Identity property: $a + 0 = a$; $a \times 1 = a$
- Inverse property: $a + (-a) = 0$; $a \neq 0$, $a \times \frac{1}{a} = 1$
2. What are the key formulas for Class 9 Maths?
The key formulas for Class 9 Maths cover various chapters. For the Number System topic, important formulas include:
- Representation of irrational numbers: E.g., $\sqrt{2}, \sqrt{3}$
- Rationalization: $\frac{1}{\sqrt{a} + \sqrt{b}} = \frac{\sqrt{a} - \sqrt{b}}{a - b}$
- Properties of exponents (laws of indices):
- $a^m \times a^n = a^{m+n}$
- $\frac{a^m}{a^n} = a^{m-n}$
- $(a^m)^n = a^{mn}$
- Decimal expansion rules for rational numbers:
- Terminating if the denominator is $2^m \times 5^n$
- Non-terminating, repeating otherwise
3. Which is the toughest chapter in class 9 math?
In CBSE Class 9 Maths, students often find the Number Systems chapter challenging due to its introduction of irrational numbers, real numbers, and concepts like irrational decimals, rationalization, and proof-based questions. However, the perception of the toughest chapter can vary among students—other challenging chapters may include Polynomials and Linear Equations in Two Variables. Vedantu's expert teachers can help clarify these concepts through interactive classes, doubt sessions, and practice worksheets.
4. What are the formulas of the number system?
The number system formulas for Grade 9 CBSE include properties and operations involving real, rational, and irrational numbers. Some crucial formulas are:
- For exponents:
- $a^m \times a^n = a^{m+n}$
- $(a^m)^n = a^{mn}$
- $a^0 = 1$ (for $a \neq 0$)
- Rationalization:
- Decimal representation:
- A rational number $\frac{p}{q}$ has a terminating decimal if $q = 2^m 5^n$ for non-negative integers $m, n$.
5. How can I quickly revise number system formulas for Class 9 exams?
To quickly revise number system formulas for Class 9 exams, students should:
- Create a summary sheet of key properties and formulas such as laws of exponents and rationalization techniques.
- Practice problems from Vedantu study materials and sample papers.
- Regularly test your understanding with MCQs and short answer questions available in Vedantu's revision notes and quizzes.
6. What are the important properties of rational and irrational numbers in class 9 number system?
Rational numbers can be expressed as $\frac{p}{q}$ where $p$ and $q$ are integers and $q \neq 0$. Their decimal representation is either terminating or non-terminating repeating. Irrational numbers cannot be represented as $\frac{p}{q}$ and their decimal expansions are non-terminating and non-repeating. Key properties include:
- Sum or product of two rational numbers is always rational.
- Sum of a rational and irrational number is always irrational.
- Product of a non-zero rational and an irrational number is always irrational.
7. How do you represent real numbers on a number line as per Class 9 syllabus?
To represent real numbers on a number line (as per Class 9 syllabus), follow these steps:
- Mark integers at equal distances.
- For rational numbers like $\frac{3}{4}$, divide the segment between 0 and 1 into 4 equal parts and count three parts from zero.
- For irrational numbers like $\sqrt{2}$, construct a right triangle with legs of 1 unit each from 0; the hypotenuse will have length $\sqrt{2}$. Use a compass to mark this distance from zero on the number line.
8. What tips does Vedantu offer for mastering number system concepts in CBSE Class 9?
Vedantu recommends these strategies for mastering number system concepts in CBSE Class 9:
- Attend interactive classes for step-by-step explanations of concepts like rationalization and decimal expansions.
- Use smart revision tools, such as flashcards for formulas.
- Consistently solve topic-wise sample papers and previous year questions.
- Clarify doubts with Vedantu’s expert teachers through one-on-one sessions.
9. What is the difference between terminating and non-terminating decimals in number systems?
Terminating decimals are decimals that come to an end after a finite number of digits (e.g., $\frac{1}{4} = 0.25$). Non-terminating decimals go on forever without ending. These are further divided into:
- Repeating decimals (e.g., $\frac{1}{3} = 0.333...$), which have a pattern.
- Non-repeating decimals (e.g., $\sqrt{2} = 1.4142...$), with no repeating pattern, indicating irrational numbers.
