# CBSE Class 9 Maths Revision Notes Chapter 1

## Class 9 Mathematics Revision Notes for Number Systems of Chapter 1

Extramarks provides Class 9 Mathematics Chapter 1 – Number System revision notes that are easily accessible to assist students in understanding the chapter’s core ideas. With these revision notes, students can quickly revise all the chapter’s topics and equations. Curated by subject matter experts, these revision notes serve as reliable reference material, allowing students to quickly and efficiently evaluate all the topics of the chapter  before exams.

## Real Numbers and their Decimal Expansions

The two cases of decimal expansions are as follows:

1. Remainder becomes zero
• Terminating is a decimal expansion of numbers whose remainder becomes zero at some step.
• For example: 7/8=0.875, with some further steps, the remainder becomes zero.
1. Remainder never becomes zero
• Non-terminating decimal expansions are those in which the residual never becomes zero after some step.
• It is divided into non-terminating recurring and non-terminating non-recurring.
• Non-terminating recurring numbers are those that keep repeating the same value after the decimal point.

For example: 9/11=0.818181….

• Non-terminating non-recurring numbers are those that do not keep repeating the same value after the decimal point, yet the remainder never becomes zero.

For example: Value of π=3.141592653589793283…

• Decimal expansion of rational numbers can be terminating or non-terminating.
• Irrational number decimal expansion is non-terminating non-recurring.

## Operations on Real Numbers

Real numbers can be multiplied, divided, added, and subtracted.

For example:

Add 2 + 3 and 2 − 23

2 + 3 + 2 − 23

=4 − 3

Subtract 2 + 3 and 2 − 23

(2 + 3) − (2 − 23

=2 + 3 − 2 + 23

=33

Multiply 22 and 33

22 × 33

=2 × 3 × 2 x 3

=66

Divide 1015 by 5

1015 / 5 = 103 × 5 / 5 = 103

Some basic facts on real-number operations are as follows:

• A rational number’s sum or difference from an irrational number is irrational.
• A non-zero rational number’s product or quotient with an irrational number will be irrational.
• When two irrationals are added, subtracted, multiplied, or divided, the outcome can be rational or irrational.

## Rationalising Denominator

Rationalising the denominator refers to the practice of making the denominator rational when it is irrational.

It is calculated by multiplying the numerator and denominator by the irrational factor in the denominator with the opposite sign.

Rationalising 12+3

12+32-32-3

2-32232

2-322– 9

2-3– 7

## Laws of Exponents for Real Numbers

There are some laws of exponent for real numbers like:

1. xm.xn=xm+n
2. xm/xn=xm−n
3. (xm)n=xmn
4. xmym= (xy) m

## 9th Class Mathematics Notes Chapter 1 Number Systems

The CBSE Class 9 Mathematics Notes Chapter 1 Number Systems are available on the Extramarks’ website. Students can gain benefit from these notes as they are provided by subject matter experts. They can access these notes whenever it is convenient for them, without having to worry about an interrupted internet connection.

### Class 9 Mathematics Chapter 1 Number Systems

The Number Systems Class 9 Notes help students recall all the numerical concepts of this chapter. It assumes that the first natural numbers began with 1. As one takes into account the 0 as well, the number set is converted to whole numbers represented by the letter W. One then returns to the number line’s negative integers, which recalls the memory of integers Z.

The next significant number classification is rational numbers. It is written in p/q form and is indicated by Q.

### Irrational Numbers

Extramarks Revision Notes guide students to revise concepts of all the number of classifications discussed so far after understanding the basic description of solved problems. Extramarks Class 9 Mathematics Notes Chapter 1 introduces students to irrational numbers. All the numbers can be represented on the number line. Similarly, regardless of classification, every point on the number line represents a number. Since those numbers are called real numbers, this principle is known as a real number line.

### Real Numbers and their Decimal Expansion

Dividing can represent every fraction in the decimal form exactly where two cases will occur.

They are as follows:

• The quotient will be equal to zero.
• The quotient will not be equal to zero.

If the numerator is divided exactly by the denominator, the quotient will be 0, but if the numerator is not divided exactly by the denominator, the quotient may not be 0.

### Representing Real Numbers on The Number Line

This section discusses how to represent real numbers on the number line. The real numbers can be seen with a magnifying glass since they are so close together, including all the points on the number line. The method of successive magnification refers to the visualisation of portraying real numbers with a magnifying glass.

### Operations on Real Numbers

This section explains all the properties of rational and irrational numbers, such as commutative, closure, identity, distributive, and so on. Few observations have been made as a result of this. They are as follows:

• The sum or difference between a rational and an irrational number is also irrational.
• All four mathematical procedures carried out by two irrational numbers could be rational or irrational.
• An irrational number is obtained from the product or quotient of a non-zero rational number and an irrational number.

### Laws of Exponents For Real Numbers

This section will cover the Law of Exponents for Real Numbers. The exponent is the number or variable that appears at the top of a digit. It is also referred to as power. The original digit is known as the base. It can be written as mn. Some solved and unsolved examples are given in these notes to help you learn exponentials in-depth and practise them further.

### Summary

Extramarks Revision Notes for CBSE Class 9 Mathematics Chapter 6 is one of the best tools a student can employ because each chapter’s content is given in an easy-to-understand format. Reading these notes helps them remember all of the concepts covered in the chapter. As a result, it will save time during exams as all the formulas are accessible from one spot.

### 1. What are rational numbers in Class 9?

Rational numbers are numbers that take the form p/q, where p and q are both integers and q is not equal to zero.

### 2. What are number systems in Mathematics?

Number state is the approach to representing numbers on the number line using a set of symbols and rules that range from 0 to 9, called digits. The number systems are classified in the Class 9 syllabus as natural numbers, whole numbers, rational numbers, irrational numbers, integers, and so on, and the first chapter covers all the relevant and basic concepts pertaining to them. Students must understand these principles thoroughly in order to understand the upcoming chapters.

### 3. Write any five rational numbers that lie between ⅗ and ⅘.

As we already saw in the chapter that rational numbers can also be represented as decimals, the given rational numbers are,

⅗ = 0.6

⅘ = 0.8.

There are numerous decimal values between 0.6 and 0.8. So, we can choose any five of them.

0.61, 0.62, 0.63, …..0.7, 0.71, 0.72, 0.73 ……0.8.

To solve the question, convert these decimal values to rational numbers.

61/100, 62/100, 63/100, ….., 7/100, 71/100,72/100…….

These are some of the rational numbers that lie between ⅗  and ⅘.

Hence, it is solved.