Expanded Form and Standard Form of a Number
Expanded Form
To write a number in its expanded form, we just write the place
values of all the digits with plus (+) sign starting from the highest place.
For example, 765349 = 7 × 1,00,000
+ 6 × 10,000 + 5 × 1000 + 3 × 100 + 4 × 10 + 9 × 1
= 7,00,000 +
60,000 + 5,000 + 300 + 40 + 9
Example 1: Write the following numbers in
expanded form.
a. 2565935 b. 796435429
Solution:
a. 2565935 = 20,00,000 + 5,00,000 + 60,000 + 5,000 + 900 + 30 + 5
b. 796435429 = 70,00,00,000 +
9,00,00,000 + 60,00,000 + 4,00,000 + 30,000 + 5,000 + 400 + 20 + 9
Standard Form
When we write a number in its short form,
we call it the standard form of a number.
For example, the standard form of 80,00,000
+ 6,00,000 + 20,000 + 1,000 + 900 + 30 + 4 is 8621934.
To write a number from expanded form
to standard form, we can use two methods.
1. We can make a place value table and put the digits in the place value table as follows.
|
TL |
L |
TTh |
Th |
H |
T |
O |
|
8 |
6 |
2 |
1 |
9 |
3 |
4 |
Now, we can write the number as 8621934.
2. We can add the place values of each digit by writing them in columns as follows.
|
TL |
L |
TTh |
Th |
H |
T |
O |
|
8 |
0 |
0 |
0 |
0 |
0 |
0 |
|
|
6 |
0 |
0 |
0 |
0 |
0 |
|
|
|
2 |
0 |
0 |
0 |
0 |
|
|
|
|
1 |
0 |
0 |
0 |
|
|
|
|
|
9 |
0 |
0 |
|
|
|
|
|
|
3 |
0 |
|
|
|
|
|
|
|
4 |
|
8 |
6 |
2 |
1 |
9 |
3 |
4 |
Example 2: Write
the following in standard form.
a. 30,00,000 + 8,00,000 + 70,000 + 2,000 + 500 + 10 + 9
b. 80,00,00,000 + 2,00,00,000 + 20,00,000
+ 9,00,000 + 30,000 + 1,000 + 400 + 90 + 4
Solution:
a. 30,00,000 + 8,00,000 + 70,000 + 2,000 + 500 + 10 + 9
|
TL |
L |
TTh |
Th |
H |
T |
O |
|
3 |
8 |
7 |
2 |
5 |
1 |
9 |
Thus, the number in the standard
form is 38,72,519.
b. 80,00,00,000 + 2,00,00,000 + 20,00,000 + 9,00,000 + 30,000 + 1,000 + 400 + 90 + 4
|
TC |
C |
TL |
L |
TTh |
Th |
H |
T |
O |
|
8 |
2 |
2 |
9 |
3 |
1 |
4 |
9 |
4 |
Related Topics:
Forming and Rounding off Numbers