Expanded Form

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 $2 \times 100 + 2 \times 10 + 5 \times 1$. 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:

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

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

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. Below table is small example:

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 place value and represent the number in the form of $\mathtt{digit} \times \mathtt{place~~value}$.

• Step 4: At last, write all the numbers as the sum of $\mathtt{digit} \times \mathtt{place~~value}$ 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 1: 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.

$9 \times 10 + 0\times 1$

Step 4: Expanded form is 90 + 0

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

Example 2: What is the expanded form of 10000?

Solution:

Step 1: The standard form of a number is 10000.

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\times 10000 + 0\times 1000 + 0\times 100 +0\times 10 + 0\times 1$

Step 4: Expanded form is 10000 + 0 + 0 + 0 + 0.

Finally, the expanded form of 10000 is 10000 + 0 + 0+ 0 + 0

Example 3: What is 45673 in expanded form?

Solution:

Step 1: The standard form of the number is 45673.

Step 2: The place value of the given number is:

4 – Ten thousand

5 – Thousands

6 – Hundreds

7 – Tens

3 – Ones

Step 3: Multiply the given number by its place value.

(i.e.,) $4\times 10000 + 5\times 1000 + 6\times 100 +7\times 10 + 3\times 1$

Step 4: Expanded form is 40,000+ 5000+600+70+3

Finally, the expanded form of the number 45673 is 40,000+ 5000+600+70+3.

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 the increasing exponent value of $\dfrac{1}{10}$. 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:

$\Rightarrow 5\times[\frac{1}{10}]+ 4\times[\frac{1}{10}]^{2} +7\times[\frac{1}{10}]^{3}\\$

$\Rightarrow 5\times[\frac{1}{10}]+ 4\times[\frac{1}{100}] + 7\times[\frac{1}{1000}]$

$ \Rightarrow 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 $7\times 10 + 8\times 1 = 70 + 8$

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

The expanded form of 235 is

$\Rightarrow 2\times[\frac{1}{10}]+ 3\times[\frac{1}{10}]^{2} + 5\times[\frac{1}{10}]^{3}\\$

$\Rightarrow 2\times[\frac{1}{10}]+ 3\times[\frac{1}{100}] + 5\times[\frac{1}{1000}]$

$ \Rightarrow 0.2 + 0.03 + 0.005$

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

Expanded Exponential Form

The expanded exponential form, the place value of the digits is represented in terms of the powers of 10 that means one’s place is represented by $10^{0}$, tens place is represented by $10^{1}$ hundreds of places are represented by $10^{2}$ and so on.

Example: The expanded exponential form of 3425 is represented by:

Solution: The expanded exponential form of 3425 is given below:

3 – Thousands $(3\times 10^{3})$

4 – Hundreds $(4\times 10^{2})$

2 – Tens $(2\times 10^{1})$

5 – Ones $(5\times 10^{0})$

Thus, the expanded exponential form of 2325 is $(3\times 10^{3}) + (4\times 10^{2}) +(2\times 10^{1}) + (5\times 10^{0})$

Solved Examples

1. What is 6783 in the expanded form?

Solution:

The place value of each digit is identified with the help of the place value chart.

Therefore $6783 = 6\times 1000 + 7\times 100 + 8\times 10 + 3\times 1 = 6000 + 700 + 80 + 3.$ Therefore the expanded form is 6000 + 700 + 80 + 3.

2. In the expanded form of the number 7569023 the digit 9 represents which place value.

Solution:

Let us expand the given number i.e, $759023 = 7\times 10,0000 + 5\times 10000 + 9\times 1000 + 0 \times 100 + 2\times 10 + 3\times 1$. Therefore, the digit 9 represents 9000 and the answer is ‘Thousand’.

3. What is the result of given expanded form $3\times 10000 + 6\times 1000 + 5\times 10$

Solution:

The result given expanded form is 36,050

Practise Problems

1. Which shows 54,679 in expanded form?

a) 5+4+6+7+9

b) 500,000+4,000+60+79

c) 50,000+4,000+600+70+9

d) 50,000+400+60+70+9

2. Fill the missing value 94,294 = 90,000 + 4,000 + _____ + 90 + 4

a) 2,000

b) 20

c) 2

d) 200

3. Which shows 48,725 in expanded form?

a) 40,000+8,000+700+20+5

b) 40,000+800+700+20+5

c) 4+8+7+2+5

d) 4,000+800+700+5

4. What is the missing number in 8,746?

8,000 + ____ + 40 +6

a) 700

b) 500

c) 40

d) 9,346

Answer

1) c

2) d

3) a

4) a

Conclusion

In this article we have learnt about the expanded form of different types like expanded form numbers,decimal forms and exponential forms. We have also learnt in the expanded form of decimals while writing the number in expanded form (for decimals) , we need to multiply each decimal digit with the increasing exponent value of $\dfrac{1}{10}$. In number as we move from the right to the left, the value of a digit increases. We have also solved problems with each given concept to test your understanding. You can solve the practical problems and check your answer accordingly.