Numeration Systems

Number system can be easier with detailed solution. Get CBSE Class 6 Mathematics Numeration Systems Notes based on NCERT Syllabus.

Indian System of Numeration

In Indian number system, ten symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 are used to write a number.

Each of these ten symbols is called a digit. Out of these digits:
i) 0, 2, 4, 6 and 8 are even numbers
ii) 1, 3, 5, 7 and 9 are odd numbers

According to Indian Numeration System, first comma comes after three digits from the right and the next comma comes after every two digit.

For a given number, we start from the extreme right as Ones, Tens, Hundreds, Thousands, Ten Thousands, Lakhs, Ten Lakhs, etc.

In Indian system to read and write a large number with ease, number is split up into groups or periods.

PERIOD Place Value Number Zeroes
Ones Ones 1 0
Tens Tens 10 1
Hundreds Hundreds 100 2
Thousands Thousands 1,000 3
Ten- Thousands 10,000 4
Lakhs Lakhs 1,00,000 5
Ten-Lakhs 10,00,000 6
Crores Crores 1,00,00,000 7
Ten-Crores 10,00,00,000 8

1. Periods are not written in plural
2. The word ‘and’ is not used before tens and ones
3. Do not put commas while writing the numeral.
4. While reading a number, all digits in the same period are read
together and the name of the period (except the ones) is read
along with it.

Example: Write the following in words according to Indian
Numeration system

            i) 3673458               ii) 945329 

PERIOD Lakhs Thousands Ones
  Ten
Lakhs
Lakhs Ten
Thousands
Thousands Hundreds Tens Ones
i) 3 6 7 3 4 5 8
ii)   9 4 5 3 2 9

i) Thirty six lakh seventy three thousand four hundred fifty eight

ii) Nine lakh forty five thousand three hundred twenty nine


   Example: Write the numerals and place the commas.
   i)          Six crores two lakh twenty one thousand two hundred sixty
                three.
   ii)          Seven lakh nine thousand nine hundred nineteen

 

PERIOD Crores Lakhs Thousands Ones
  Ten
Crores
Crores Ten
Lakhs
Lakhs Ten
Thousands
Thousands Hundreds Tens Ones
i)   6 0 2 2 1 2 6 3
ii)       7 0 9 9 1 9

    i) 6,02,21,263                 ii) 7,09,919

 

International System of Numeration

According to International System of Numeration, the first comma is placed after the hundreds place and the next commas are placed after every three digits and this grouping of number is called period.

In International System of Numeration we use ones, tens, hundreds, thousands, millions and billions.

PERIOD Place Value Number Zeroes
Ones Ones 1 0
Tens Tens 10 1
Hundreds Hundreds 100 2
Thousands Thousands 1,000 3
Ten- Thousands 10,000 4
Hundred-Thousands 100,000 5
Millions Million 1,000,000 6
Ten Million 10,000,000 7
Hundred Million 100,000,000 8
Billions Billion 1,000,000,000 9
Ten Billion 10,000,000,000 10
Hundred Billion 100,000,000,000 11

While reading a number in this system, all digits in the same period
are read together and the name of the period (except the ones) is
read along with it.

Example: Write the following in words according to International
Numeration system
 

           i) 45145879632                                ii) 61346987

PERIOD Billions Millions Thousands Ones
  Ten
Billions
Billions Hundred
Millions
Ten
Millions
Millions Hundred
Thousands
Ten
Thousands
Thousands Hundreds Tens Ones
i) 4 5 1 4 5 8 7 9 6 3 2
ii)       6 1 3 4 6 9 8 7

 

i) Forty five billion one hundred forty five million eight hundred seventy nine thousand six hundred thirty two
ii) Sixty one million three hundred forty six thousand nine hundred eighty seven.

 

Example: Write the numerals and place the commas.
i) Forty two million two hundred eighty seven thousand four hundred fifty seven
ii) Five million thirty six thousand nine

PERIOD Millions Thousands Ones
  Hundred
Millions
Ten
Millions
Millions Hundred
Thousands
Ten
Thousands
Thousands Hundreds Tens Ones
i)   4 2 2 8 7 4 5 7
ii)     5 0 3 6 0 0 9

 

               i) 42,287,457                       ii) 5,036,009

Effect of grain size on piezoelectric, ferroelectric and dielectric properties of PMN-PT ceramics.

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