Expanded Form and Standard Form of a Number

# Expanded Form and Standard Form of a Number

## Expanded Form and Standard Form of a Number

### Expanded Form

In expanded form, a number is written according to the place value of its digits.

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

Thus, the number in the standard form is 86,21,934.

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

Thus, the number in the standard form is 82,29,31,494.

Related Topics:

Expanded Form of Decimals

Forming and Rounding off Numbers

Comparing and Ordering Integers

Operations on Integers