A decimal number system is the number system that we use on a daily basis based on the 10 digits. In mathematics, a number system is considered the notation of numbers by using digits or symbols. The decimal number system is also known as the Hindu-Arabic or Arabic number system since in ancient civilizations it was difficult to multiply and divide large numbers by using hands.

## Definition

### What is the Decimal Number System?

In the **decimal number system**, the numbers are represented with base 10. The way of denoting the decimal numbers with base 10 is also termed as decimal notation. This number system is widely used in computer applications. It is also called the base-10 number system which consists of 10 digits, such as, 0,1,2,3,4,5,6,7,8,9. Each digit in the decimal system has a position and every digit is ten times more significant than the previous digit. Suppose, 25 is a decimal number, then 2 is ten times more than 5. Some examples of decimal numbers are: ^{1}

(12)_{10}, (345)_{10}, (119)_{10}, (200)_{10}, (313.9)_{10}

A number system which uses digits from 0 to 9 to represent a number with base 10 is the decimal system number. The number is expressed in base-10 where each value is denoted by 0 or first nine positive integers. Each value in this number system has the place value of power 10. It means the digit at the tens place is ten times greater than the digit at the unit place. Let us see some more examples: ^{1}

(92)_{10} = 9×10^{1}+2×10^{0}

(200)_{10} = 2×10^{2}+0x10^{1}+0x10^{0}

The decimal numbers which have digits present on the right side of the decimal (.) denote each digit with decreasing power of 10. Some examples are: ^{1}

(30.2)_{10}= 30×10^{1}+0x10^{0}+2×10^{-1}

(212.367)_{10} = 2×10^{2}+1×10^{1}+2×10^{0}+3×10^{-1}+6×10^{-2}+7×10^{-3}

### Definition of Decimal Number System

Decimal number system is the number system we use every day and uses digits from 0 – 9, i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, & 9. The base number of the decimal number system is 10 as the total number available in this number system is 10. If any number is represented without a base, it means that its base is 10. ^{2}

## References

^{1} “Decimal Number System (Definition, Conversions & Examples)”. 2022. *BYJUS*. https://byjus.com/maths/decimal-number-system/.

^{2} “Decimal Number System – Definition, Conversion, Examples, FAQs”. 2022. *CUEMATH*. https://www.cuemath.com/numbers/decimal-number-system/.

## Additional Reading

⭐ “Decimal Number System – GeeksForGeeks”. 2020. *GeeksForGeeks*. https://www.geeksforgeeks.org/decimal-number-system/.

“What Is A Decimal? – Math Review (Video)”. 2013. *Mometrix*. https://www.mometrix.com/academy/decimals/.

## Videos

⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.