Partitioning (3 Digits)

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Basics on the topicPartitioning (3 Digits)

In mathematics, the value of a digit is determined by its position in a number. This principle is called 'place value'. It distinguishes the importance of ones, 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 maths operations. Therefore, learning about the 3-digit expanded form will help you understand the arithmetic processes better.

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

Every 3-digit number is composed of ones, 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 furthest to the right. Identify its value. The last digit, 7, represents the ones. It is worth 7 ones.
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 of 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, when expressing three digit numbers in expanded form, we follow the same steps and never skip zeros:

• Step one: always start with the number furthest 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?

Partitioning (3 Digits) exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Partitioning (3 Digits).
• How can three digit numbers be partitioned?

Hints

The steps go in the order of the place value chart. Which place comes first, next and last?

Find the value of each place before you write the partitioned number.

Solution

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

Let's try to partition the number: 462.

1. Show 462 using 4 hundreds blocks, 6 tens blocks, and 2 ones blocks.
2. Count the hundreds blocks and find the value of the digit. In the number 462, 4 is in the hundreds place and 4 groups of 100 = 400. The value of the hundreds place in this example is 400.
3. Count the tens blocks to find the value of the digit. In the number 462, 6 is in the tens place and 6 groups of 10 = 60. The value of the tens place in this example is 60.
4. Count the ones blocks to find the value of the digit. In the number 462, 2 is in the ones place and 2 groups of 1 = 2. The value of the ones place in this example is 2.
5. Write the partitioned form of 462 by adding the values of each place together. 462 = 400 + 60 + 2.
• How do we partition 537?

Hints

This is 537 represented with base ten 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.

Solution

537 partitioned is 500 + 30 + 7.

First count the hundreds blocks, then the tens blocks, and 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 partitioned form of 537.

500 + 30 + 7 = 537

• What do these blocks represent?

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 partitioned form.

To partition 791:

• 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 group of 1 is 1.
• This number partitioned is: 700 + 90 + 1 = 791
Here are how place value blocks should represent the remaining partitioned numbers:
• 200 + 30 + 6 = 236, should be shown with 2 hundreds blocks, 3 tens blocks, and 6 ones blocks.
• 400 + 50 + 8 = 458, should be shown with 4 hundreds blocks, 5 tens blocks, and 8 ones blocks.
• 300 + 20 + 1 = 321, should be shown with 3 hundreds blocks, 2 tens blocks, and 1 ones blocks.
• Can you find the pairs?

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.
• Add them altogether to make the partitioned number.

If there are no blocks for a place value, we don't write it in the partitioned number.

For example, there are no hundreds here, so we just write 10 + 5 = 15.

Solution
• The image with 7 tens and 4 ones (as shown above) represents 70 + 4 = 74.
• The image with 1 hundred and 9 ones represents 100 + 9 = 109.
• 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 this order, which stands for Hundreds, Tens, and Ones. Remember, you Have To Order correctly to write the partitioned number.

Solution

Here we can see:

• The hundreds place highlighted in violet
• The tens place highlighted in blue
• The ones place highlighted in green
We always see hundreds, tens and ones in this order in a place value chart.

• How would we represent 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.
• Finally, count the value of the ones blocks.
• Add them all together (thousands + hundreds + tens + ones).

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

Solution

These are the base ten blocks that represent 2,435 partitioned. 2,000 + 400 + 30 + 5

• 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 partitioned number is: 2,000 + 400 + 30 + 5 = 2,435.