Expanded Form

Dhristi JEE 2022-24

Expanded Form in Detail

In Mathematics, an expandable form is a process of splitting or partitioning numbers into their correct place values. The expandable form enables us to understand large numbers in a better way. For example, let us take the number 79498845. It is difficult to understand this number. Here, an expandable form enables us to understand each of the digits based on their place values. For example, let us consider the simple number 225 and try to understand its expanded form.

In expanded form, 225 is written as  2 x 100 + 2 x 10 + 5 x 1. It implies that there are two hundred, two tens, and 5 ones in this number. We can easily understand the meaning of each digit of a number with its expanded form.

Learning a number with a higher number of digits is quite difficult without knowing its expanded form. The expandable form enables us to understand the building blocks of higher numbers. Each of the digits in large numbers can be written as 1,10, 100, 1000,10000, and so on. Read on to learn more about what is the expanded form of a number.


What is an Expanded Form?

The expandable form obtains the number as a sum, where each digit is a separate term multiplied by its place value.

Example:

943 = 9 x 100 + 4 x 10 + 3 x 1. This is because there are 900 hundred, 4 tens, and 3 ones.

943 = 9 hundreds, 4 tens, 3 ones = 9(100) + 4 (10) + 3.

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Each digit in the number has a place value. It determines the value of that digit according to its position in the number. As we move towards the right from the left, the value of a digit in a number increases. This implies that the digit on the left has a lower place value than the digit on the right.


2

1

5

6

2

8

6

Million

Hundred

Thousands 

Ten Thousand

Thousands

Hundreds

Tens

Ones

Value of the Digit Increases


How to Write Numbers in Expanded Form?

Following are the steps to write the numbers in expanded form.

  • Step 1: Write the standard form of a number

  • Step 2: Identify the place value of a given number using the place value chart.

  • Step 3: Multiply each digit by its pace value and represent the number in the form of (digit place value).

  • Step 4: At last, write all the numbers as the sum of (digit place value) form, which is the expanded form of a number.

Let us more clearly understand the above steps with an example. Take a look at the below.


Example:

What is the Expanded Form of 90?

Solution:

Step 1:  The standard form of a number is 90.

Step 2: The place value of a given number is 

9 tens

0 ones

Step 3: Multiply each digit of a  given number by its place value.

9 x 10 + 0 x 1

Step 4: Expanded form is 90 + 0

Finally, the expanded form of 90 is 90 + 0.


What is the Expanded Form of 10,000?

Solution:

Step 1: The standard form of a number is 10,000.

Step 2: The place value of a given number is 

1 Ten Thousands

0 Thousands

0 Hundreds

0 tens

0 ones

Step 3: Multiply each digit of a  given number by its place value.

1 x 10,000 + 0 x 1000 + 0 x 100 + 0 x 10 + 0 x 0.

Step 4: Expanded form is 10,000 + 0 + 0 + 0 + 0.

Finally, the expanded form of 10,000 is 10,000 + 0 + 0+ 0 + 0


Expanded Form of Decimal Numbers

The decimal number can also be written in expanded form. While writing the number in expanded form, we need to multiply each decimal digit with its increasing exponent value of 1/10. Let us try to understand the expanded form of a decimal number with an example. 


1. Write the Decimal Number 0.547 in Expanded Form.

Solution:

0.547 can be written as:

= 5 x (1/10) + 4 x (1/10)² + 7 x (1/10)³.

= 5 x (1/10) + 4 x (1/100) + 7 x (1/1000).

= 0.5 + 0.04 + 0.007

Therefore, the expanded form of 0.547 is 0.5 + 0.04 + 0.007


2. Write the Decimal Number 78.235 in Expanded Form.

Solution:

First, write the expanded form of a number before the decimal place.

The expanded form of 78 is 7 x 10 + 8 x 1 = 70 + 8

Now, write the expanded form of a number after the decimal place.

The expanded form of 235 is

= 2 x (1/10) + 3 x (1/10)² + 5 x (1/10)³.

= 2 x (1/10) + 3 x (1/100) + 5 x (1/1000).

= 0.2 + 0.03 + 0.005

Therefore, the expanded form of 78.235 is 70 + 8 + 0.2 + 0.03 + 0.005.

FAQs on Expanded Form

1. What Does Expanded Form Mean?

Ans: The expanded form of the number is written as a sum, with each digit making an individual term multiplied by its place value. For example, 729 has a expanded form of 7  x 100 + 2 x 10 + 9 and 4213 has a expanded form of 4 x 1000 + 2 x 100 + 1 x 10 + 3.

Generally, the expanded form helps understand the meaning of place value. Also, it can be useful in thinking of different number bases other than 10.

2. Why is it Important to Learn the Expanded Form?

Ans: Expanded form is important because it enables one to identify the place value of each digit in the given number.

3. What is the Difference Between Expanded Notation and Expanded Form?

Ans: Expanded notation and expanded form are not the same. In the expanded notation, a number is represented as the sum of each digit in a number multiplied by its respective place value whereas, in the expanded form, the only addition is used between the place value numbers. 

For example: 

Expanded Form of 343: 300 + 40 + 3

Expanded Notation of 343: (3 x 100) + (40 x 10) + 3

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