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## Class 9 Maths Number System Formulas

The number system is a base 10 number system in which each digit has a value of 10^n, where n is the position of the digit from the rightmost digit (the units digit). The number 987 can be represented as 9 * 10^2 + 8 * 10^1 + 7 * 10^0. The value of a number can be determined by taking the sum of the products of each digit and its corresponding power of 10.

## What is a Number?

A number is a mathematical value used for counting or measuring or labelling objects. Numbers are used to performing arithmetic calculations. Examples of numbers are natural numbers, whole numbers, rational and irrational numbers, etc. 0 is also a number that represents a null value.

A number has many other variations such as even and odd numbers, prime and composite numbers. Even and odd terms are used when a number is divisible by 2 or not, whereas prime and composite differentiate between the numbers that have only two factors and more than two factors, respectively.

In a number system, these numbers are used as digits. 0 and 1 are the most common digits in the number system, that are used to represent binary numbers. On the other hand, 0 to 9 digits are also used for other number systems. Let us learn here the types of number systems.

## Types of Number System

There are various types of number systems in mathematics. The four most common number system types are:

- Decimal number system (Base- 10)
- Binary number system (Base- 2)
- Octal number system (Base-8)
- Hexadecimal number system (Base- 16)

Now, let us discuss the different types of number systems with examples.

### Decimal Number System (Base 10 Number System)

The decimal number system has a base 10 because it uses ten digits from 0 to 9. In the decimal number system, the positions successive to the left of the decimal point represent units, tens, hundreds, thousands and so on. This system is expressed in decimal numbers Every position shows a particular power of the base (10).

Example of Decimal Number System:

The decimal number 1457 consists of the digit 7 in the units position, 5 in the tens place, 4 in the hundreds position, and 1 in the thousands place whose value can be written as

(1×10^{3}) + (4×10^{2}) + (5×10^{1}) + (7×10^{0})

(1×1000) + (4×100) + (5×10) + (7×1)

1000 + 400 + 50 + 7

1457

### Binary Number System (Base 2 Number System)

The base 2 number system is also known as the binary number system wherein, only two binary digits exist, i.e., 0 and 1. Specifically, the usual base-2 is a radix of 2. The figures described under this system are known as binary numbers which are the combination of 0 and 1. For example, 110101 is a binary number.

We can convert any system into binary and vice versa.

## Number System Class 9

The number system is a way of representing numbers using digits. The number system we use is called base 10, because it uses 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. The number 26 can be represented as:

2 × 10 + 6 = 26

In this number, 2 is the base, 10 is the multiplier, and 6 is the exponent. The number 26 can also be represented as:

2 × 100 + 6 = 26

In this number, 2 is the base, 100 is the multiplier, and 6 is the exponent. The number 26 can also be represented as:

2 × 1000 + 6 = 26

In this number, 2 is the base, 1000 is the multiplier, and 6 is the exponent.

## Important Number System Formula Class 9

We know that a number system is a way of representing numbers using symbols. In a number system, each symbol represents a certain value.

The number system we use to represent numbers in everyday life is the decimal number system. In the decimal number system, each symbol represents a certain power of 10.

The number 10 is called the base of the number system. In the decimal number system, the base is 10. This means that the value of each symbol is based on 10 multiplied by the power of the symbol.

For example, in the number 123, the 1 represents 10 multiplied by 1, or 10. The 2 represents 10 multiplied by 2, or 20. The 3 represents 10 multiplied by 3, or 30. And so on.

In the number system, each symbol represents a certain value.

The number system we use to represent numbers in everyday life is the decimal number system. In the decimal number system, each symbol represents a certain power of 10.

The number 10 is called the base of the number system. In the decimal number system, the base is 10. This means that the value of each symbol is based on 10 multiplied by the power of the symbol.

For example, in the number 123, the 1 represents 10 multiplied by 1, or 10. The 2 represents 10 multiplied by 2, or 20. The 3 represents 10 multiplied by 3, or 30. And so on.