Last updated on July 25th, 2025
The expanded form is a way of expressing the value of each number on its place value. Understanding large numbers becomes easier when the number is expressed in expanded form. The expanded form helps us to know the building blocks of higher numbers. Let us now see more about expanded form in the following topic.
Expanded form can be defined as a method of separating expressions or numbers into their parts. It involves expressing an algebraic statement as the sum of its terms in an expression or the place values in a number, and breaking down decimal numbers according to their place values. The exact process of “expanding” varies depending on whether algebraic expressions or numbers are involved. The following table shows the numbers and their expanded forms:
Number |
Ten Thousand |
Thousands |
Hundreds |
Tens |
Ones |
11 |
10 | 1 | |||
253 |
200 |
50 | 3 | ||
9852 |
9000 |
800 |
50 | 2 | |
54852 |
50000 |
4000 |
800 |
50 | 2 |
Place value refers to the value that a digit in a number represents based on where it falls in the number. It finds out how much each digit contributes to the number's total value. Each position in a multi-digit integer corresponds to a power of 10. For example, the place value of the given digit 78,205 is:
7 is in the ten thousands place (70000)
8 is the thousands place (8000)
2 is in the hundreds place (200)
0 is the tens place (0)
5 is in the units place (5)
To write numbers in expanded form, below-mentioned steps are followed -
Step 1: First write the number in standard form.
Step 2: Identify the place values for each digit.
For example, in the number 6,745
6 is in Thousands place (6000)
7 is in Hundreds place (700)
4 is tens place (40)
5 is in units place (5)
Step 3: Multiply the place values with their respective digits.
(6 × 1000), (7 × 100), (4 × 10), (5 × 1)
Step 4: Represent all the numbers as the sum of the product of the digit and their place value (digit × place value).
(6 x 1000) + (7 x 100) + (4 x 10) + (5 x 1)
Step 5: Represent the number in the Expanded Form
The expanded form of 6,745 is 6000 + 700 + 40 + 5.
To write the expanded form of whole numbers, we have to follow the following steps:
To understand the steps better, let us consider an example.
Find the expanded form of 4,221
Step 1: In the number 4,221, the digits are in the thousands, hundreds, tens, and ones places.
4 (Thousands) + 2 (Hundreds) + 2 (Tens) + 1 (Units)
Step 2: Then, express each digit in terms of its place value and add them up.
4 x 1000 + 2 x 100 + 2 x 10 + 1 x 1
Step 3: After that, simplify it by performing the multiplications.
4000 + 200 + 20 + 1
Step 4: At last, the individual numbers are combined to get the final expanded form.
4000 + 200 + 20 + 1 = 4221
In the table below, we can see the expanded form:
Number |
Thousands |
Hundreds |
Tens |
Ones |
4221 | 4 | 2 | 2 | 1 |
To write the expanded form of decimal numbers, the following steps are -
To understand the steps better, let us consider an example.
Find the expanded form of 3.692
Step 1: In the number 3.692, the digits are in the tenths, hundredths, and thousandths places.
3 (Whole Part) + 6 (Tenths) + 9 (Hundredths) + 2 (Thousandths).
Step 2: Then, express each digit after the decimal point in terms of its place value.
3 x 1 + 6 x 0.1 + 9 x 0.01 + 2 x 0.001
Step 3: After that, simplify it by performing the multiplications.
3 + 0.6 + 0.09 + 0.002
Step 4: At last, the individual numbers are combined, to get the final expanded form.
3 + 0.6 + 0.09 + 0.002 = 3.692
In the below table, we can see the expanded form:
The expanded form has numerous applications across various fields. Let us explore how the expanded form is used in different areas:
Education and Learning: In elementary mathematics classes, expanded forms are taught for a strong foundation. Suppose 345 is written as 300+40+5, where the number is represented by the sum of the place value of the digits. This concept helps in calculating any problem easily. If a number is broken down into manageable parts, it becomes easier to estimate sums, differences, or products.
Financial Literacy and Budgeting: Expanded form is applied in financial contexts to help break down and understand large numbers. When budgeting, expenses can be decomposed into thousands, hundreds, tens, and ones, making it easier to grasp the magnitude of expenses or savings. This clarity supports better financial planning and more informed budgeting decisions.
Bill Payment or Breakdown of Tax: E-commerce platforms have become a part of our lives. While buying any items online, we pay the bill amount directly. In the bill, most of the components are written in detail for easy access. Like in a bill, GST, Service Tax, Discounts, Offers all these amounts are mentioned differently for the customer use.
Students tend to make mistakes while understanding the concept of expanded form. Let us see some common mistakes and how to avoid them, in expanded form:
Write 502 in expanded form.
502 = 500 + 0 + 2
Determine the place values:
5 in the hundreds, 0 in the tens, 2 in the ones.
Multiply each digit by its place value:
5×100=500
0×10=0
2×1=2
Write as a sum:
500+0+2
Write 1001 in expanded form.
1001 = 1000 + 0 + 0 + 1
Identify the digits and their places:
1 in the thousands, 0 in the hundreds, 0 in the tens, 1 in the ones.
Express each digit accordingly:
1×1000=1000
0×100=0
0×10=0
1×1=1
Combine the terms:
1000+0+0+1
Write 7682 in expanded form.
7682 = 7000 + 600 + 80 + 2
Determine place values:
7 in the thousands, 6 in the hundreds, 8 in the tens, 2 in the ones.
Multiply each digit by its corresponding place value:
7 × 1000 = 7000
6 × 100 = 600
8 × 10 = 80
2 × 1 = 2
Write the number as the sum:
7000 + 600 + 80 + 2
Write 93 in expanded form.
93 = 90 + 3
Identify the digits:
9 in the tens, 3 in the ones.
Multiply:
9×10=90
3×1=3
Sum the products:
90+3
Write 205 in expanded form.
205 = 200 + 0 + 5
Identify the place values:
2 in the hundreds, 0 in the tens, 5 in the ones.
Multiply:
2×100=200
0×10=0
5×1=5
Combine the values:
200+0+5
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
: She loves to read number jokes and games.