Indian System of Numeration

Place Value Chart according to Indian System of Numeration.

In Indian system we start grouping the number from right in group of 3 and further in group of 2.
The place value chart have been separated into groups called periods i.e. ones, thousands, lakhs and crores.

Reading of number according to Indian System of Numeration

In Indian System of Numeration periods such as ones, thousands, lakhs, crores, etc. are used so that number can be easily read.

Let’s read the below number according to Indian System of Numeration

11, 54, 08, 453

First put the number in their respective places.

This number is read as eleven crore fifty four lakh eight thousand four hundred fifty three.

Marking periods according to Indian System of Numeration

Different periods like ones, thousands, lakhs and crores are separated by comma (,) starting from the right to differentiate the periods.
We start with the first period, named as ones period, consist the first three digits of the given number.
The second period (i.e. thousands period), consist of the next two digits of the given number.
The third period (i.e. lakhs period), consist of the next two digits of the given number. The fourth period (i.e. crores period), consist of the next two digits of the given number.

Let’s differentiate periods by placing commas in between.

Example: 457833228

This number is separated by comma as 45, 78, 33, 228

Place Value and Face Value

Place Value of a digit is the value of the digit depending on it's position in the number.
Place value of a digit is obtained by multiplying the face value of the digit with its corresponding value of the place in that number.
Face Value of the digit is the digit itself.

Example: 88, 45, 11, 009

Expanded Form and Standard Form

When each digit of a given number is written with its place value, then the number is written as the sum of place value of each digit in the number. Then we get the expanded form of that number.

Example: 34, 16, 97, 832

We can expand any given number in three ways:

3 ten crore + 4 crore + 1 ten lakh + 6 lakh + 9 ten thousand + 7 thousand + 8 hundred + 3 ten + 2 one

3 x 10,00,00,000 + 4 x 1,00,00,000 + 1 x 10,00,000 + 6 x 1,00,000 + 9 x 10,000 + 7 x 1,000 + 8 x 100 + 3 x 10 + 2 x 1

30,00,00,000 + 4,00,00,000 + 10,00,000 + 6,00,000 + 90,000 + 7,000 + 800 + 30 + 2

Successor and Predecessor

To find the successor of a given number, we add 1 to the number.
To find predecessor of a given number, we subtract 1 from the number.

Example:

Successor of 99,99,999 is

99,99,999 + 1 = 1,00,00,000

Predecessor of 4,00,00,000 is

4,00,00,000 – 1 = 3,99,99,999

Ascending order

The arrangement of numbers from the smallest to the greatest is called ascending order. This is also called as increasing order.

Example: 88,88,870 < 7,54,34,108 < 67,65,76,676 < 67,76,78,676

Descending order

The arrangement of numbers from the greatest to the smallest is called descending order. This is also called as decreasing order.

Example: 67,76,78,676 > 67,65,76,676 > 7,54,34,108 > 88,88,870

Forming greatest and smallest number from given digits.

Numbers can be formed using the given digits with or without repetition of digits.

Example: 0,1,3,5,6,7,8,and 9

Greatest 8 digit number from above digits is 9,87,65,210
Smallest 8 digit number from above digits is 1,02,56,789

Practice Exercise

Q1) Write the number names according to the Indian System of Numeration.

1,35,67,234 - ______________________________________________

41,00,15,000 - _______________________________________________

6,10,00,030 - ______________________________________________

75,00,11,045 - _______________________________________________

Q2) Write the numeral according to the Indian System of Numeration.

Twenty crore thirty nine lakh seventy thousand six hundred seventeen. _________________.

Five crore thirteen lakh fifty thousand and twelve. __________________

Seventy five crore forty one lakh twenty five thousand four hundred nine.___________________

Six crore six lakh five thousand six. __________________

Q3) Write in numerals in words.

The largest 8 digit number. ________________________

The smallest 7 digit number._________________________

Q4) Write the place value and face value of the digits 3 and 4.

1,35,67,214 - ______________________________________________

41,00,15,003 - _______________________________________________

6,40,00,030 - ______________________________________________

35,00,11,045 - ______________________________________________

Q5) Write in expanded form.

5,00,28,876

____________________________________________________________

12,34,56,789

____________________________________________________________

Q6 ) Write in short form (standard form).

5 ten crore + 5 crore + 7 ten lakh + 4 lakh + 0 ten thousand + 6 thousand + 3 hundred + 5 tens + 3 ones = _________________

20,00,00,000 + 7,00,00,000 + 80,00,000 + 6,00,000 + 90,000 + 5,000 + 700 + 70 + 7 =___________________

8 x 10,00,00,000 + 7 x 10,00,000 + 7 x 1000 + 6 x 10 + 8 x 1 =______________________

Q7) Write the numeral in figures.

10 lakh more than 56,56,889 ________________________

20 thousand less than 1,77,780 ________________________

1 lakh more than 5,00,111 ________________________

Q8) Write the place value of underlined digits.

1,35,67,214 - ______________________________________________

41,00,15,003 - _______________________________________________

6,40,00,030 - ______________________________________________

35,00,11,045 - ______________________________________________

Q9) Write in ascending order.

55,23,89,888; 56,42,67,450; 58,14,24,112; 57,00,00,321

____________________________________________________________

5,00,00,000; 4,50,00,000; 6,05,00,400; 5,05,55,555

____________________________________________________________

Q10) Write in descending order.

9,15,20,704; 9,18,22,709; 8,12,45,700; 9,17,23,714

____________________________________________________________

66,50,30,000; 3,99,99,999; 8,99,99,999; 37,60,20,800

____________________________________________________________

Q11) Write greatest and smallest possible number using the given digits without repeating digits.

2, 0, 1, 7, 8, 4, 9

__________________ ___________________

3, 0, 1, 5, 8, 4, 9

__________________ ___________________

Q12) Complete the series.

10,12,10,100; 11,12,10,100; 12,12,10,100; _________________

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