Numeral System

Numeral System

Numeral System or System of Numeration:- A Numeral System or System of Numeration is a writing system for expressing number.
There are three types of numeral system-
1. Decimal Numeral System- Use in measuring and counting
2. Roman Numeral System- Use in notation
3.Binary Numeral System-Use in computer only

  Before discussing about system we have to know some key points-

Digit:- Digits are a single symbol used to make a numeral.
      e.g.- In decimal system the numeral 2 is made up of only one digit 2.

Number:- A number is a mathematical object used to count, measure or label. or in other words we can say " A number is a unit that forms part of system of counting and calculating.
    e.g.- 10, 25, 555, etc all are numbers.

In this section we will discuss about Decimal Numeral System.

Decimal Numeral System:- Decimal Numeral System is based on 10 digits that is 0, 1, 2, 3, 4, 5, 6,                                                 7, 8 and 9.
       This system is of two types-
(a) Hindu Arabic System of Numbers
(b) International System of Numbers

(a) Hindu Arabic System of Numbers:- This numeral system is originated in India in 6th or 7th               century. This system is a set of 10 digits that is 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 that represents a               number in decimal numeral system.
                                  We can read or write a number correctly by the place value of a digit on the                basis of its position in the number.
                                In the Hindu Arabic Numeration system place value of  digit go in the sequence of  Ones, Tens, Hundreds, Thousands, Ten thousands, lakhs, Ten lakhs, Crores, Ten crores etc.

 Writing in this system:-
           When we are going to write a number, must focus on placing comma (,)
(i) After writing all the digits place first comma after three digits from the rightmost.
(ii) Then all the commas are placed after two digits after the first comma.
   e.g.- 19,23,456

Reading in this system:-
 (i) If there is only three digit or less then we read it in first group.

       e.g.- 435, 

            there is three digit which can be read in one group i.e. Ones

              We read it as "Four hundreds thirty five"

(ii) If there is more than three digit then we should take two or more groups.

       e.g.- suppose a number 1,23,456

Group	Lakhs	Thousands		Ones
Place value	Lakhs	Ten thousands	Thousands	Hundreds	Tens	Ones
Number	1	2	3	4	5	6

   

We read this number as "One lakhs twenty three thousands four hundred fifty six".

(b) International System of Numbers:- Every country has its own numeration system due to which it was very difficult to understand  the numbers in other country by one. So, In 1947, Union government concerned that there should be another system of numeration all over the world in which everyone can show the numbers.

                             We can read or write a number correctly by the place value of a digit on the basis            of  its position in the number.
                             In the International Numeration system place value of  digit go in the sequence of            Ones, Tens, Hundreds, Thousands, Ten thousands, Hundred thousands, Million,  etc.

Writing in this system:-

                           When we are going to write a number, must focus on placing comma (,)
      (i) In International numeration system all the commas are placed after every three digits from the rightmost.
e.g.- 123,456
        24,376,847

Reading in this system:- 
  (i) If there is only three digit or less then we read it in first group.

       e.g.- 435, 

            there is three digit which can be read in one group i.e. Ones

              We read it as Four hundreds thirty five

  (ii) If there is more than three digit then we should take two or more groups.

       e.g.- suppose a number 123,456

Group	Thousands			Ones
Place value	Hundred thousands	Ten thousands	Thousands	Hundreds	Tens	Ones
Number	1	2	3	4	5	6

We read this number as "One hundred twenty three thousands four hundred fifty six"

Relation between Hindu Arabic Numeral System and International Numeral System:-  We can relate both numeration system together-

 e.g.- 1 Million=10 Lakhs

         10 Billion= 10 Arab

Relation between Hindu Arabic Numeral System and International Numeration System
International Numeration System	Numeral	International Numeration System
Ones	1	Ones
Tens	10	Tens
Hundreds	100	Hundreds
Thousands	100,0	Thousands
Ten thousands	100,00	Ten thousands
Hundred thousands	100,000	Lakhs
Million	100,000,0	Ten lakhs
Ten million	100,000,00	Crores
Hundred million	100,000,000	Ten crores
Billion	100,000,000,0	Arab
Ten billion	100,000,000,00	Ten arab
Hundred billion	100,000,000,000	Kharab
Trillion	100,000,000,000,0	Ten kharab
Ten trillion	100,000,000,000,00	Neel
Hundred trillion	100,000,000,000,000	Ten neel
Quadrillions	100,000,000,000,000,0	Padam
Ten quadrillions	100,000,000,000,000,00	Ten padam
Hundred quadrillions	100,000,000,000,000,000	Shankh
Quintillions	100,000,000,000,000,000,0	Ten shankh
Ten quintillions	100,000,000,000,000,000,00	-----
Hundred quintillions	100,000,000,000,000,000,000	-----

Relation within same System:- Sometimes you have heard a different types of numbers like "Fifteen hundred", what will you understand by this number. Here we will relate such type of numbers in the same system with different place values.

 e.g.- 10 hundred=10,00=1thousand=1,000

      here 10 hundred is not the correct in reading or writing but we use sometimes in our daily life. some other examples are-

    15 hundred= One thousand five hundred=1,500

    100 tens= 1 thousands=1,000

    1000 million=1 billion=1,000,000,000