Decimal Number System

Decimal Number System

Hello!!!

Before we discuss about the decimal number system ; we should introduce ourselves with the 'numbers' and 'number systems'.

Number

Generally , a mathematical object which is used to count , label and measure ; is called a number.

There are mainly two different types of numbers: Imaginary numbers  and   Real numbers.

Number system

The way of representing numbers is called a number system.

Different types of number systems

The number systems are mainly subcategories into :
Decimal or positional number system;

Hexadecimal number system;

Octal number system;

Binary number system.

 Now we will discuss about the Decimal number system.

       

Decimal number system

This system is mostly used in calculations and measurements worldwide.

 Brief history:

 World's first decimal multiplication table was made from bamboo slips, in the time period  305 BC; during the

Warring States period in China.

Many ancient cultures calculated with numerals based on ten, sometimes argued due to human hands (as, human hands has total ten fingers) typically having ten digits.

   Some non-mathematical ancient books

  like  "Vedas" dating back to 1900–1700 BCE make use of decimals.

  The Egyptian hieratic numerals, the Greek alphabet numerals, the Hebrew alphabet numerals, the Roman numerals, the Chinese numerals and early Indian Brahmi numerals are all non-positional decimal systems, and required large numbers of symbols.

Descripton:

 The base-10 or decimal number system contains ten single digits:

  0, 1, 2,3,4,5,6,7,8,9.

 But we can't use only the single digits for any requirement. So, their permutations and combinations are made for fullfill our requirements.

 To write 10 or more, we use 2 or more digits. Each of the digits of a higher value is associated with a place value. Each of these place values is associated with a power of ten.

   Thousands   Hundreds  Tens  Ones/units

    10³                   10²          10¹       10⁰

      A general expansion of a decimal number:  aₙ,...a₁,a₀ ,b₁ ,b₂..., bₙ is as follows:

 aₙ×10ⁿ + ...+a₁×10¹ +a₀×10⁰+ b₁×10⁻¹ +...+bₙ×10⁻ⁿ.

 As for example, 19= 1×10 + 9×10⁰.
                               112=1×10² + 1×10¹+2×10⁰.

How  do we build or devlop decimal  numbers?

   It is very easy to write the single digit decimal numbers(0-9). But mathematics can not think in single digits. We need multi-digit numbers for daily  calculations.
 So, we are devloping the number system.
   Let's take an example.
 when we write the  number next to 9 ; we just  make it a number with two digits by adding 1 to the left side and make the right side 0. So, the next number to 9 becomes 10.
The next numbers are devloped by just replacing the right most digit with 1,2,..  upto 9. When we reach a number with right most digit 9; we add 1 with the left most digit and make the other digits 0. This gives the next number. As for example 20 is the next number to 19. In this way we are getting the next number. We are increasing! We are devloping!

It is needless to talk about the necessity of decimal numbers. We are using decimal numbers almost everywhere in our daily life. Actually we are living  in decimals!

  

 If you find out any incorrect information or know anything more about this , please write it in the comment section!