How to Write Numbers in Expanded Form

Writing numbers in expanded form is the process of breaking a larger number down into the sum of each digit multiplied by its corresponding place value. For example, the number 2,397 written in expanded form would be 2,397 = 2,000 + 300 + 90 + 7.

What is Expanded Form in Math?

In math, expanded form is when you take a number and break it down into the sum of each digit multiplied by its corresponding place value.

For example, you can rewrite the number 236 in expanded form as follows:

• 236 = 200 + 30 + 6

In other words, the number 236 can be expressed as the sum of 2 hundreds, 3 tens, and 6 ones. Figure 01 below illustrates how we can use money to conceptualize what expanded form is in math.

If you understand this concept of expanded form as simply rewriting a number as the sum of each digit multiplied by its place value, then you can express any number, big or small, in expanded form.

So, if you wanted to write the number 7,469 in expanded form, you would just have to identify the place value of each digit:

• 7 → thousands

• 4 → hundreds

• 6 → tens

• 9 → ones

So, 7,469 = 7,000 + 400 + 60 + 9

The table below further illustrates how we expressed the number 7,469 in expanded form.

Now that you have an understanding of what is expanded form in math, let’s work through a few step-by-step examples of writing numbers in expanded form.

How to Write Numbers in Expanded Form Examples

Example #1: Write in Expanded Form: 83

For our first example, we will learn how to write a two-digit number in expanded form.

For the number 83, we know that:

• The first digit (8) is in the tens place

• The second digit (3) is in the ones place

So, we can multiply each digit by its place value as follows:

• 8 x 10 = 80

• 3 x 1 = 3

And, finally, we can rewrite the number 83 in expanded form as follows:

• 83 = 80 + 3

Final Answer: 83 = 80 + 3

Expanded Form Example #2

Example #2: Write in Expanded Form: 456

For our second example, we will write a three-digit number in expanded form.

For the number 456, we know that:

• The first digit (4) is in the hundreds place

• The second digit (5) is in the tens place

• The third digit (6) is in the ones place

So, we can multiply each digit by its place value as follows:

• 4 x 100 = 400

• 5 x 10 = 50

• 6 x 1 = 6

So, we can express 456 in expanded form as follows:

• 456 = 400 + 50 + 6

Final Answer: 456 = 400 + 50 + 6

Expanded Form Example #3

Example #3: Write in Expanded Form: 6,873

Are you starting to get the hang of writing numbers in expanded form? Let’s try another example where we have to write a four-digit number in expanded form.

For the number 6,873, we know that:

• The first digit (6) is in the thousands place

• The second digit (8) is in the hundreds place

• The third digit (7) is in the tens place

• The fourth digit (3) is in the ones place

So, we can multiply each digit by its place value as follows:

• 6 x 1,000 = 6,000

• 8 x 100 = 800

• 7 x 10 = 70

• 3 x 1 = 3

Now, we can express 6,873 in expanded form as follows:

• 6,873 = 6,000 + 800 + 70 + 3

Final Answer: 6,873 = 6,000 + 800 + 70 + 3

Expanded Form Example #4

Example #4: Write in Expanded Form: 25,129

In this example, we have to write a five-digit number in expanded form, where:

• The first digit (2) is in the ten-thousands place

• The second digit (5) is in the thousands place

• The third digit (1) is in the hundreds place

• The fourth digit (2) is in the tens place

• The fifth digit (9) is in the ones place

Next, we can multiply each digit by its place value as follows:

• 2 x 10,000 = 20,000

• 5 x 1,000 = 5,000

• 1 x 100 = 100

• 2 x 10 = 20

• 9 x 1 = 9

Now, we can express 25,129 in expanded form as follows:

• 25,129 = 20,000 + 5,000 + 100 + 20 + 9

Final Answer: 25,129 = 20,000 + 5,000 + 100 + 20 + 9

Expanded Form Real-World Problem

Example #5: A minor league baseball team sold 1,654 tickets online for $10 each and another 6,088 tickets at the gate for $13 each. Write the total revenue for tickets sold in expanded form.

To solve this real-world expanded form problem, we have to first calculate the total revenue of tickets sold as follows:

• Online Ticket Sales: 1,654 x 10 = 16,540

• Gate Ticket Sales: 6,088 x 13 = 79,144

• Total Revenue: 16,540 + 79,144 = 95,684

Now that we know that total revenue ($95,684), we can solve the problem by writing it in expanded form:

• The first digit (9) is in the ten-thousands place

• The second digit (5) is in the thousands place

• The third digit (6) is in the hundreds place

• The fourth digit (8) is in the tens place

• The fifth digit (4) is in the ones place

Next, we can multiply each digit by its place value as follows:

• 9 x 10,000 = 90,000

• 5 x 1,000 = 5,000

• 6 x 100 = 600

• 8 x 10 = 80

• 4 x 1 = 4

So, 95,684 can be expressed in expanded form as:

• 95,684 = 90,000 + 5,000 + 600 + 80 + 4

Final Answer: $95,684 = $90,000 + $5,000 + $600 + $80 + $4

Numbers in Expanded Form Interactive Quiz

Are you ready to test your understanding of how to write numbers in expanded form? If so, go ahead and try the free interactive 5-question quiz below and see how many questions you can answer correctly.

At the end of the quiz, you will receive your score:

• If you score an 80% or higher, you likely have a strong understanding of how to write numbers in expanded form.

• If you score lower than 80%, you should go back and work through this guide again to strengthen your skills.

Expanded Form Worksheets

Expanded Form FAQ

What is expanded form?

In math, expanded form is an alternate way of rewriting a number in standard form by breaking it down into the sum of each digit multiplied by its corresponding place value.

For example, you can rewrite the number 4,563 in expanded form as follows:

• 4,563 = 4,000 + 500 + 60 + 3

Where:

• The first digit (4) is in the thousands place value slot.

• The second digit (5) is in the hundreds place value slot.

• The third digit (6) is in the tens place value slot.

• The fourth digit (3) is in the ones place value slot.

So, we can multiply each digit by its place value as follows:

• 4 x 1,000 = 4,000

• 5 x 100 = 500

• 6 x 10 = 60

• 3 x 1 = 3

Which is why we can say that 4,563 = 4,000 + 500 + 60 + 3.

What does expanded form mean?

In math, expanded form is a method for expressing a number in standard form as the sum of each digit multiplied by its corresponding place value.

For example, the expanded form expression 800 + 200 + 9 means 829 (because the sum of 800, 200 and 9 is 829).

How do I write a number in expanded form?

You can write any number in expanded form by identifying the place value slot of each digit, multiplying each digit by its corresponding place value, and expressing the result as a sum.

For example, if you wanted to write 5,362 in expanded form, you would start by identifying each digit’s place value:

• The first digit (5) is in the thousands place

• The second digit (3) is in the hundreds place

• The third digit (6) is in the tens place

• The fourth digit (2) is in the ones place

Next, multiply each digit by its place value as follows:

• 5 x 1,000 = 5,000

• 3 x 100 = 300

• 6 x 10 = 60

• 2 x 1 = 20

Finally, you can express 5,362 in expanded form as follows:

• 5,362 = 5,000 + 300 + 60 + 20