# Number Systems Class 9 Notes

# Chapter 1 Number Systems

Developed by expert Vidyakul faculty, the NCERT Class 9 Maths Chapter 1 Math notes help students effectively and proficiently solve problems while preparing for Council exams. These notes also make the task easier for students to understand.

The number system tells about the origin and history of numbers, integers, rational numbers, continuous and non-repeating decimal fractions, and properties of irrational numbers. Vidyakul provides over 470 exercises covering all the sub topics covered in Chapter 1.

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### MATHEMATICS CLASS 9th NOTES CH-1

### Points to Remember

Some of the important points related to Number Systems have been mentioned below for the quick reference of students.

Natural Numbers: These are the counting numbers (1, 2, 3,1, 2, 3, etc.).

Whole Numbers: The set of numbers that includes all natural numbers and the number zero are called whole numbers. Whole numbers are also called Non-Negative Integers.

Prime Numbers: A natural number larger than 11 is a prime number if it does not have other divisors except for itself and 11. (The lowest prime number is 22. 22 is also the only even prime number. The lowest odd prime number is 33.)

Composite Numbers: It is a natural number that has at least one divisor different from unity and itself.

Even Numbers: An even number is an integer that can be divided by two and remain an integer or has no remainder.

Odd Numbers: An integer that is not an even number is an odd number.

Divisibility Tests:

(i) Divisibility by 22 or 55: A number is divisible by 22 or 55 if the last digit is divisible by 22 or 55.

(ii) Divisibility by 33 (or 99): All such numbers, the sum of whose digits are divisible by 33 (or 99), are divisible by 33 (or 99).

(iii) Divisibility by 44: A number is divisible by 44 if the last 22 digits are divisible by 44.

(iv) Divisibility by 66: A number is divisible by 66 if it is simultaneously divisible by 22 and 33.

(v) Divisibility by 88: A number is divisible by 88 if the last 33 digits of the number are divisible by 88.

### Topics and Sub-topics

These exercises are easy to understand and will give students a useful foundation for their entrance exams in the long run. Students will face a variety of challenges that help develop problem-solving skills. Students are encouraged to watch the video tutorials in this chapter before proceeding with troubleshooting.

At Vidyakul, students will find answers to all the questions in this exercise. All notes are provided free of charge and students have free access to NCERT videos, NCERT examples, Vidyakul explainers, and more. Now, let us know the important topics covered in Class 9 Maths Chapter 1:

Natural Numbers: These are the counting numbers (1, 2, 3,1, 2, 3, etc.).

Whole Numbers: The set of numbers that includes all natural numbers and the number zero are called whole numbers. Whole numbers are also called Non-Negative Integers.

Prime Numbers: A natural number larger than 11 is a prime number if it does not have other divisors except for itself and 11. (The lowest prime number is 22. 22 is also the only even prime number. The lowest odd prime number is 33.)

Composite Numbers: It is a natural number that has at least one divisor different from unity and itself.

Even Numbers: An even number is an integer that can be divided by two and remain an integer or has no remainder.

Odd Numbers: An integer that is not an even number is an odd number.

Divisibility Tests:

(i) Divisibility by 22 or 55: A number is divisible by 22 or 55 if the last digit is divisible by 22 or 55.

(ii) Divisibility by 33 (or 99): All such numbers, the sum of whose digits are divisible by 33 (or 99), are divisible by 33 (or 99).

(iii) Divisibility by 44: A number is divisible by 44 if the last 22 digits are divisible by 44.

(iv) Divisibility by 66: A number is divisible by 66 if it is simultaneously divisible by 22 and 33.

(v) Divisibility by 88: A number is divisible by 88 if the last 33 digits of the number are divisible by 88.

Learn more about the types of number systems in Number System Class 9 Notes pdf.

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