Expanded Form

• A number when expressed with its place value denotes its expanded form.
• Suppose we write a number 619, here we actually mean that we have a total of 600 + 10 + 9. This expansion shows the value of each of its digit and hence represents the expanded form.
• The expanded form varies in the Indian and International structure as per their defined period.

International Place Value System

Examples:  

Expand the following numbers as per International Place Value System:

(a) 81,664

(b) 1,697,832

We can expand any given number in three ways:

(a) 81,664

= 8 ten thousand + 1 thousand + 6 hundred + 6 ten +
4 one

Or = 8 x 10,000 + 1 x 1,000 + 6 x 100 + 6 x 10 + 4 x 1

Or= 80,000 + 1,000 + 600 + 60 + 4

(b) 1,697,832

= 1 million + 6 hundred thousand + 9 ten thousand +
7 thousand + 8 hundred + 3 ten + 2 one

Or = 1×1,000,000 + 6×100,000 + 9×10,000 + 7x
1,000 + 8 x 100 + 3 x 10 + 2 x 1

Or = 1,000,000 + 600,000 + 90,000 + 7,000 + 800 + 30 +
2

Indian Place Value System

Examples:  

Expand the following numbers as per Indian Place Value System:

(a)  64,980

(b)  9,82,143

We can expand any given number in three ways:

(a)   64,980

= 6 ten thousand + 4 thousand + 9 hundred + 8 ten +
0 one

Or = 6 x 10,000 + 4 x 1,000 + 9 x 100 + 8 x 10 + 0 x 1

Or = 60,000 + 4,000 + 900 + 80 + 0

(b)   9,82,143

= 9 lakh + 8 ten thousand + 2 thousand + 1 hundred +
4 ten + 3 one

Or = 9 x 1,00,000 + 8 x 10,000 + 2 x 1,000 + 1 x 100 +
4 x 10 + 3 x 1

Or = 9,00,000 + 80,000 + 2,000 + 100 + 40 + 3