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Expanded Form – Definition, FAQs, Practice Problems, Examples

Jessica Kaminski

reviewed by Jo-ann Caballes

Updated on January 13, 2026

At Brighterly, we love helping your kid learn math concepts through detailed explanations and practice. In this article, we are going to look into expanded form in math.

Learning to write in expanded form is one of the key skills in early math, as it helps kids see how numbers are built and why digits matter. We will look into what expanded form is, including definition and examples, notation, methods, and much more, as well as work through some problems together. Ready? Let’s dive in!

What is an expanded form?

In this section, let’s look into the definition of expanded form, as well as some examples.

Expanded form definition

Math expanded form is a way of writing that shows the value of each number by breaking the number down into millions, thousands, hundreds, tens, and single digits.

Because of this, the expanded form of numbers and understanding of place value are strongly interconnected. In the number, each digit has its specific role, and the expanded form makes that role easier to see by highlighting its place in the number. We’ll discuss the place value in detail a bit later in the article. 

Expanded form example

Here are a few simple examples of expanded form to demonstrate your kids the process.

The number 342, for example, would be 300 + 40 + 2. 

1673 = 1000 + 600 + 70 + 3

96 = 90 + 6

16398 = 10000 + 6000 + 300 + 90 + 8

Not that hard, isn’t it?

Place value expanded form

As mentioned above, expanded numbers and place value go hand in hand. This is because the position of a digit in the number determines its value.

When writing a number in expanded form, your kid will need to use this place value to break the number into parts that are easy to see and understand. 

Let’s take the number 5482 as an example of expanded form. The number has 4 place values

• 5 thousands = 5000
• 4 hundreds = 400
• 8 tens = 80
• 2 ones = 2

So, in expanded form, the student would write it as 5,000 + 400 + 80 + 2.

Here is a helpful little chart showing how to place values in expanded form. 

How to write numbers in expanded form?

To write number in expanded form means to break a number into the value of each digit. 

Start by looking at each digit of a given number, and try to identify its place value. For example, in the number 4823, the 4 is in the thousands place (so it stands for 4000), 8 is in the hundreds place, and so on. 

Once you know the values of all the digits, you can then rewrite the number in expanded form as a sum of the parts. In the case of 4823, that would be 4000 + 800 + 20 + 3. 

Writing numbers in expanded form

When writing numbers in expanded form, we use place value to show how much each digit is worth. As you move to the left, your place value goes up by the power of 10. For example, in 12345, 1 stands for 1×10000, 2 stands for 2×1000, 3 stands for 3×100, and so on.

Expanded form of decimal numbers

Expanded form in math isn’t limited to whole numbers, but works the same way with decimals as well. 

When writing the expanded form of decimals, you simply need to move into smaller place values instead of larger ones. Similar to the whole numbers, each place to the right of the decimal point becomes ten times smaller, moving from tenths to hundreds to thousands. 

One nuance to remember here is that in the decimal world, tenths are bigger than hundreds, and so on. For example, students can write the number 3.47 as 3 + 0.4 (representing four tenths) + 0.07 (representing seven hundredths).

What is expanded notation?

So far, we looked into what is expanded form in math, and how to write it the straightforward way. However, the expanded form is not the only way to break down large numbers into their place-value components. Another method is the expanded notation. 

Expanded notation method

The expanded form breaks the number down into a simple addition. Expanded notation takes it a step further and shows the value of each digit using multiplication.

We mentioned earlier that the values in numbers grow by powers of 10, and expanded notation explicitly shows it. For example, instead of writing 5000, you would write the digit multiplied by its place value, like 5 x 1000. 

Expanded notation examples

Let’s now see how it works through the example of number 5482. To write the number in expanded notation, you take each digit and multiply it by its place value.

Then, all you need to do is combine these multiplications into an addition sequence, like so:

(5 x 1000) + (4 x 100) + (8 x 10) + (2 x 1) = 5482

If your kid is older, you can make the expanded notation more challenging for them by using exponents. We already know that each place value grows by a power of ten, so why not use that knowledge?

The expanded view using exponents will look like this:

(5 x 10³) + (4 x 10²) + (8 x 10) + (2 x 1) = 5482

Here is another example:

14673 = (1 x 10000) + (4 x 1000) + (6 x 100) + (7 x 10) +(1 x 3) = (1 x 10⁴) + (4 x 10³) + (6 x 10²) + (7 x 10) +(1 x 3)

As you can see, expanded notation is a great way to reveal and understand the internal structure of each number.

Standard form vs expanded form

Another terminology you may come across is the standard form of numbers. The difference between standard form and expanded form is that the standard form is the normal way we write numbers (like 342). And the expanded form is the “stretched” number that shows the value of each digit added together (like 300 + 40 + 2).

You can think of the standard form as the final, packaged product, while the expanded form is the detailed recipe. 

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Solved examples on expanded form

Now, let’s test how well your kid understood expanded form. Below are a few examples where they need to write numbers in expanded form. Give them a go, and check the answers.

1. Write 19253 in its expanded form.

Answer:

2. Write 8460 in its expanded form.

Answer: 

3. Write 3106 in its expanded form.

Answer:

4. Write 682 in its expanded form.

Answer: 

Practice problems on expanded form

Frequently asked questions on expanded form

What is expanded form?

An extended form is a way of writing numbers that shows the value of each digit. Instead of writing the number as a single unit, students need to break it into parts based on place value. This helps children see how hundreds, tens, ones, and decimals combine to form the whole number. 

What are expanded form examples?

Here are a couple of examples demonstrating how to write each number in expanded form.

The first example is the number 3482, which can be written as 3000+400+80+2.

Another example, this time with decimals, is 14.46, which can be written as 10+4+0.5+0.06

What is the purpose of writing numbers in expanded form?

Understanding of both expanded form and standard form helps children understand place value and see how digits come together to form a number. By understanding extended form, your child can build a stronger number sense, understand large numbers, and learn to add, subtract, and round more accurately.

How do you write numbers in expanded form?

To write each number in expanded form, your child needs to separate digits according to their place values and write them as an addition sequence. For example, in number 572, 5 represents hundreds, 7 represents tens, and 2 represents 2. So, the extended form would be 500+70+2.

Can expanded form be used for decimal numbers?

Yes, expanded form works with decimals too. The logic is the same: students break down numbers into whole numbers and fractional place values. For example, 6.43 will be 6+0.4+0.03. Working with decimals can be a bit tricky at first, but this will help students understand decimal places more clearly.

Expanded form: Worksheets

The best way to become an expanded form is through practice. You can get some fun and effective practice sessions in with free math worksheets filled with expanded form and place value puzzles. 

• Place value worksheet 3rd grade
• Expanded form worksheets
• Expanded notation worksheets
• Expanded form worksheets 2nd grade

Jessica Kaminski

86 articles

Jessica is a seasoned math tutor with over a decade of experience in the field. With a BSc and Master’s degree in Mathematics, she enjoys nurturing math geniuses, regardless of their age, grade, and skills. Apart from tutoring, Jessica blogs at Brighterly. She also has experience in child psychology, homeschooling and curriculum consultation for schools and EdTech websites.