Revise notes Class 9 number systems

Revise notes
Class 9 Maths
Number Systems

Topics

1. Number System
2. Irrational Number on Number line
3. Locate Root 3
4. Real numbers in Decimal form
5. Real number on Number Line
6. Operation on Real numbers
7. Represent Square Root of Real Number Geometrically
8. Identities related to Square root
9. Law of Exponents for Real numbers

Real numbers (both rational & irrational) can be represented in decimal form. Eg: 10/3, 7/8, √2 can be represented in decimal form. There are 3 different cases for rational number conversion to decimal form.

Rational Number

Case 1: The remainder becomes 0. E.g. : 7/8
Case 2: The remainder never becomes 0 with repetition. E.g.: 10/3

Irrational Number

Case 3:The remainder never becomes 0 with NO repetition E.g.: √2

Case 1: Rational Number, remainder becomes 0. The decimal expansion ends or terminates after finite number of steps. We call it terminating decimals. E.g.: ½ = 0.5 , 7/8= 0.875 , 5/2 = 2.5 etc

Case 2: Rational Number, The remainder never becomes 0 with repetition. E.g.: 10/3 = 3.3333333333333…… & 1/7 = 0.142857142857142857142857….

We call it non terminating recurring decimals.

We can also convert non terminating recurring decimals to rational number form.

E.g.: 0.3333333…… can be converted to p/q rational number form.

Let x= 0.33333333…. (eq 1)

Multiplying eq1 by 10 on both side, we get

10x = 3.333333333…… (eq 2)

Subtracting Eq 1 from Eq 2 we get,

9x = 3

Or x = 1/3

Thus 0.3333333…… = 1/3

Case 3: Irrational number, Remainder never becomes 0 with NO repetition E.g.: √2

We have seen that decimal expansion of a rational number is either terminating or non-terminating repeating. Thus we can also say that, if the number is either terminating or non-terminating repeating, then it is Rational number. Number whose decimal expansion is Non terminating, non-repeating is Irrational number.

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Class 9 Maths Number Systems NCERT Chapter 1 Free Notes for Best Revision

Revision of Class 9 Maths Number Systems is a crucial aspect of effective learning. Revision plays a vital role in the learning process and is especially important before exams. Here are some key points you can consider emphasizing in your content:

Retention and Memory: Regularly reviewing and revisiting the material of Class 9 Maths Number Systems helps reinforce the concepts in students' minds. It strengthens memory pathways, making it easier to recall information during exams and beyond.
Consolidation of Knowledge: When you revise notes, you are essentially consolidating your knowledge. This means connecting new information with what you already know, making the overall understanding more robust.
Identifying Knowledge Gaps: Revision allows students to identify any gaps in their understanding or areas where they need further clarification. This gives you a chance to seek help or delve deeper into those topics. For detailed understanding, you can always refer to the videos of Number Systems Class 9 Maths NCERT Chapter 1 on LearnoHub.com
Building Confidence: As you revise Number Systems Class 9 Maths and become more familiar with the content, your confidence in your abilities grows. Confidence is a crucial factor in exam performance as it reduces anxiety and allows you to approach exams with a positive mindset.
Different Revision Techniques: Use a variety of revision techniques such as summarizing notes, creating flashcards, practicing past papers, discussing concepts with peers, and teaching others. Different techniques work for different students, and it's essential to find what suits you the best. You can also attend the LIVE Revision classes on LearnoHub.com or watch the LIVE Revision Race videos of LearnoHub on Number Systems Class 9 Maths NCERT Chapter 1.
Spacing Effect: Spacing out revision sessions over time, rather than cramming all at once, has been shown to improve long-term retention. Create a revision schedule leading up to the exams to allow for spaced practice.
Regular Revision over Cramming: Regular and consistent revision throughout the academic year is very important. Waiting until the last moment to cram everything can be overwhelming and less effective than spaced-out revision.
Self-Assessment: Assess your understanding periodically through quizzes or self-tests. This helps you to gauge your progress and identify areas that need further attention. Refer Class 9 Number Systems Online Tests.
Balanced Approach: Remind students to strike a balance between revision and other activities. Adequate rest, exercise, and relaxation are essential for optimal learning and performance.
Seeking Help: If you face difficulties during the revision process, Refer the videos of Class 9 Maths Number Systems. Clearing doubts promptly is crucial for a better grasp of the subject matter. You can always ask your doubts on Number Systems Class 9 Maths NCERT Chapter 1. “Ask a Question” section of LearnoHub.com

By highlighting the benefits and strategies of effective revision, you can approach your studies more mindfully and achieve better results in your exams. Best of luck bachhon!

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Create a Distraction-Free Environment: Find a quiet and comfortable place to study where you can minimize distractions. Turn off or silence your phone, log out of social media accounts, and inform others around you that you need uninterrupted study time. A dedicated study environment will help you focus better.
Set Specific Goals: Before starting your study session, set clear and achievable goals. Break down your study material into smaller tasks, and plan what you want to accomplish during each session. Having specific goals will give you a sense of direction and purpose, making it easier to concentrate.
Use the Pomodoro Technique: The Pomodoro Technique is a time management method that involves studying in short, focused intervals, typically 25 minutes, followed by a short break of 5 minutes. After completing four sessions, take a longer break of around 15-30 minutes. This technique can improve focus and productivity by providing regular breaks to recharge.
Stay Organized: Keep your study materials, notes, and resources well-organized. Having everything you need at hand will save time and reduce distractions caused by searching for materials. Use color-coded folders or digital tools to maintain a structured study system.
Practice Mindfulness and Meditation: Before you begin studying, take a few minutes to practice mindfulness or meditation. Deep breathing exercises and clearing your mind of distractions can help you approach your study session with a calm and focused mindset.

Remember, studying with full concentration is a skill that takes time and practice to develop. If you find your mind wandering during study sessions, gently bring your focus back to the task at hand and be patient with yourself. With consistent effort, you can improve your ability to concentrate and make the most of your study time.

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