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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
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