# Expanded Form

## Expanded Form – Definition

In this learning text we will be introducing the expanded form. Firstly, let’s look at the definition of place value and expanded form as well as expanded form examples.

• Place value describes the position of a digit in a number. For example, in the number 345, the digit 3 is in the hundreds place, 4 is in the tens place, and 5 is in the ones place. When we write numbers in expanded form, we use place values to break down the number.

• The expanded form is a way of writing a number as the sum of the place value of its digits. In the expanded form, we must break up a number to the place value of digits and expand it to show the value of each digit. For example, the expanded form of 345 is 300 + 40 + 5.

## Expanded Form of Whole Numbers

Writing numbers in expanded form shows the value for each digit so it is easy to recognize ones, tens, hundreds, etc place value.

Look at the example below where we use the place value chart and base 10 blocks to identify the value of each place in a number.

In our example we will count the first hundred blocks to identify the hundreds place value, we have three hundred blocks which is equal to three hundred. Next, we count the ten blocks to identify the tens place value, we have four ten blocks which is equal to forty. In our last step we count the last blocks to identify ones pace value, we have five ones blocks which is equal to five.

H T O
300 40 5

Finally, we can write the number in expanded form using the addition symbol between each place value. The number 345 in expanded form is three hundred plus forty plus five.

We will look at one more example and make sure you understand fully how to write a number in expanded form.

## Expanded Form – Example

This time we will look at a number 237 and by breaking the number into hundreds, tens and ones. Let’s count the first hundred blocks to identify the hundreds place value, we have two hundred blocks which is equal to two hundred. Next, we count the ten blocks to identify the tens place value, we have three ten blocks which is equal to thirty. Last step is to count the blocks to identify one's pace value, we have seven blocks which is equal to seven. Finally, we can write the number in expanded form using the addition symbol between each place value. The number 237 in expanded form is two hundred plus thirty plus seven.

## Expanded Form of Whole Numbers – Summary

How to write a number in expanded form? Look at the summary below:

• 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 symbols between places values.
Step# What to do
1 Identify the hundreds place value.
2 Identify the tens place value.
3 Identify the ones place value.
4 Write the number in expanded form using
the addition symbols between places values
.

Now you should be able to write a number in expanded form. If you need more help, please watch the video explaining addition with expanded form and complete the worksheet on expanded form.