## Topic outline

• ### Indian System of Numeration

• Indian System of Numeration

Place Value Chart according to the 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) is 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

Example: 88, 45, 11, 009

Expanded Form and Standard Form

When each digit of a given number is written with its place value, we get the expanded form of the 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

Or

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

Or

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 it and to find predecessor of a given number, we subtract 1 from it.

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