# Expanded Form (3 Digits)

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Expanded Form (3 Digits)
CCSS.MATH.CONTENT.2.NBT.A.3

## 3 Digit Numbers – Expanded Form

In mathematics, the value of a digit is often determined by its position in a number. This principle is called 'place value'. It distinguishes the importance of units, tens, and hundreds.

Expanded form is a method that breaks down numbers based on their place value. It provides a clearer understanding of the value of each digit in a number.

This technique is frequently used in number decomposition, understanding place value, and basic math operations. Therefore, learning about the 3-digit expanded form will help you understand the arithmetic processes better and will make you the master of numbers.

## How to Break Down a 3-Digit Number? – Method

Every 3-digit number is composed of units, tens, and hundreds. To express a number in its expanded form, you will have to identify each digits’ place value.

For instance, let's take the number 237:

Step # What to do In this example:
1 Always start with the number farthest to the right. Identify its value. The last digit, 7, represents the units. It is worth 7 units.
2 Now look at the second number from the right. Identify its value. The middle digit, 3, stands for the tens place. This means it actually represents 30 (3 tens or 3 x 10).
3 Then look at the remaining number, which is furthest to the left. Identify its value. The first digit, 2, is in the hundreds place. Therefore, it represents 200 (2 hundreds or 2 x 100).
4 Express the number in expanded form Now, to express the number 237 in its expanded form:
237 = 200 + 30 + 7

As you can see, by identifying the place values and breaking down the number, we've expanded 237 to show the value of each individual digit. Have a look at the chart below for a depiction the number 237 in expanded form:

Hundreds Tens Ones
2 3 7

## Common Mistakes in 3-Digit Expanded Form and How to Avoid Them

Attention to detail is crucial. Common errors include misplacing digits or overlooking the zeros in a number. If you spot a zero in the middle or end of the number, take extra care not to skip it!

## Expanded Form for 3-Digit Numbers – Conclusion

The concept of 3-digit expanded form is not just a mathematical technique; it's a tool for clearer comprehension of place value.

Remember, that when expressing numbers in expanded form, we follow the same steps and never skip zeros:

• Step one: always start with the number farthest to the right. Identify its value.

• Step two: look at the second number from the right. Identify its value.

• Step three: look at the remaining number, which is furthest to the left. Identify its value.

• Step four: Express the number in expanded form

What is the main purpose of learning expanded form?
Can I use the expanded form concept for numbers beyond three digits?
Why is zero important in the expanded form?
How is expanded form different from standard form?
What's the next step after mastering 3-digit expanded form?

### TranscriptExpanded Form (3 Digits)

Skylar and Henry have received a special delivery. The parts of their new item are in hundreds, tens, and ones blocks "Grab the instructions Henry, let's build this thing!" While they build it, let's learn all about expanded form - three digits. When writing numbers in expanded form, we are writing to show the value of each place in a number. How do we write a three digit number in expanded form? We can use a place value chart and base ten blocks to identify the value of each place in a three digit number. First, count the hundreds blocks to identify the hundreds place value. Here, we have three hundreds blocks, which represents three hundred. Next, count the tens blocks to identify the tens place value. Here, we have four tens blocks, which represents forty. Then, count the ones blocks to identify the ones place value. Here, we have five ones blocks, which represents five. Finally, write the number in expanded form using the addition symbol between each place value. Three hundred forty-five in expanded form is three hundred plus forty plus five! Let's explore the number of pieces in Skylar and Henry's package! Two hundred thirty-seven pieces are in the box. First, count the hundreds blocks to identify the value of the number in the hundreds place. What is the value of the hundreds place? There are two hundreds blocks in the hundreds place, so it is two hundred. What is the next step? Next, count the tens blocks to identify the value of the number in the tens place. What is the value of the tens place? There are three tens blocks in the tens place, so it is thirty. What is the last step? Finally, count the ones blocks to identify the value of the number in the ones place. What is the value of the ones place? There are seven ones blocks in the ones place, so it is seven. What is the expanded form of two hundred thirty-seven? When we write two hundred thirty-seven in expanded form, we write it as two hundred plus thirty plus seven. The box has two hundred thirty-seven blocks in all! Before we check out what Skylar and Henry built, let's review. Remember, to write numbers in expanded form, first, count the hundreds blocks to identify the hundreds place value. Next, count the tens blocks to identify the tens place value. Then, count the ones blocks to identify the ones place value. Finally, write the number in expanded form using the addition symbol between place values. "Henry, this is fantastic craftsmanship if I say so myself!" "It really is, Skylar!"

## Expanded Form (3 Digits) exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Expanded Form (3 Digits).
• ### How can numbers be written in expanded form?

Hints

First you need to show the number with place value blocks.

After you show the number with place value blocks, you need to count to find how many hundreds, tens, and ones.

Solution

To write a number in expanded form, you must first find the value of each place and then add them together.

Let's try to write the expanded form of the number: 462.

1. Show 462 using 4 hundreds blocks, 6 tens blocks, and 2 ones blocks.
2. Count the hundreds, tens, and ones blocks and find the value of the digit: there are 4 groups of 100, so 400. There are 6 groups of ten, so 60. There are 2 groups of one, which is just 2.
3. Write the values of 400, 60, and 2 down.
4. Put a plus sign to make 400 + 60 + 2
• ### Determine the expanded form of a three-digit number.

Hints

This is 537 represented with place value blocks. What is the value of each place value column?

The value of each place is written at the bottom of the chart. Add the hundreds, tens, and ones values together to make the expanded form of 537.

Solution

To solve for the expanded form of 537, first count the hundreds blocks, then the tens blocks, then the ones blocks, to find the value of each place:

• The value of 5 hundreds blocks is 500.
• The value of 3 tens blocks is 30.
• The value of 7 ones blocks is 7.
Add all of the values together in order to show the expanded form of 537.

500 + 30 + 7 = 537

• ### Identify expanded form with place value blocks.

Hints

Remember to count your groups in the order of the place value chart: hundreds, tens, and ones.

These place value blocks show 400 + 10 + 7 = 417.

Solution

Count the value of the hundreds blocks, tens blocks, and ones blocks. Then add them together to create the expanded form.

To write the number 791 in expanded form:

• The 7 is in the hundreds place, so the value of 7 groups of 100 is 700.
• The 9 is in the tens place, so the value of 9 groups of 10 is 90.
• The 1 is in the ones place, so the value of 1 groups of 1 is 1.
• Together, we would write the expanded form as: 700 + 90 + 1 = 791
Here are how place value blocks should represent the remaining numbers written in expanded form:
• The expanded form, 200 + 30 + 6 = 236, should be shown with 2 hundreds blocks, 3 tens blocks, and 6 ones blocks.
• The expanded form, 400 + 50 + 8 = 458, should be shown with 4 hundreds blocks, 5 tens blocks, and 8 ones blocks.
• The expanded form, 300 + 20 + 1 = 321, should be shown with 3 hundreds blocks, 2 tens blocks, and 1 ones blocks.
• ### Determine expanded form given a group of place value blocks.

Hints

Count the groups of red hundreds blocks by 100. Count the groups of blue tens blocks by 10. Count the groups of green ones blocks by 1. Then, add them altogether to make the expanded form!

If there are no groups of hundreds, tens, or ones, remember that 0 should hold its place! If there is a 0 in the hundreds place, you don't need to write it at all.

For example, in the number 15 above, there are no groups of hundreds, 1 group of ten, and 5 groups of one. So, the expanded form is just 10 + 5 = 15.

Solution

To solve for expanded form, you must always find the value of the hundreds place, tens place, and ones place. Then, write the expanded form using an addition sign in between each place.

• The image with 1 hundred and 9 ones represents 100 + 9 = 109.
• The image with 7 tens and 4 ones represents 70 + 4 = 74.
• The image with 3 hundreds, 5 tens, and 1 one represents 300 + 50 + 1 = 351.
• The image with 6 hundreds, 2 tens, and 8 ones represents 600 + 20 + 8 = 628.
• ### Identify the order of a place value chart.

Hints

In the chart, H means hundreds, T means tens, and O means ones. Highlight your chart in the same order.

In a place value chart, you always see H T O in order, which stands for Hundreds, Tens, and Ones. Remember, you Have To Order correctly to write in expanded form.

Solution

A place value chart always goes in the same order: groups of hundreds blocks, groups of tens blocks, and groups of ones blocks. This is the same order that you write expanded form.

• ### Determine the expanded form of a four-digit number.

Hints

Count the value of the thousands blocks first. Then, count the value of the hundreds blocks. Next, count the value of the tens blocks. Last, count the value of the ones blocks. Add them all together to create expanded form (thousands + hundreds + tens + ones = expanded form).

Be sure to go in order of the place value chart. It now begins with the largest valued group: TH or thousands.

Solution

How to solve for the expanded form of 2,435:

• There are 2 groups of 1,000, which have a value of 2,000.
• There are 4 groups of 100, which have a value of 400.
• There are 3 groups of 10, which have a value of 30.
• There are 5 groups of 1, which have a value of 5.
• When we add these groups together, the expanded form is: 2,000 + 400 + 30 + 5 = 2,435.