Expanded Form Lesson

In the last lesson, we covered the topic of Place Value. We learned how to set up a place value chart, which helps to identify the place of each digit in a given number. When we dig further into the topic of place value, we learn that we can write a number in a manner that shows the value of each digit. This method is known as expanded form or expanded notation. To write a number in expanded form, simply form the sum of each digit multiplied by its corresponding place value. Let's use our place value chart and look at a few examples.
Example 1: Write the number 259 in expanded notation.
We can begin by placing 259 into the place value chart; this will give us the place value for each digit in the number.

• 2 - Hundreds
• 5 - Tens
• 9 - Ones

Now that we know the place values, we can write the number in expanded form. Again form the sum of each digit multiplied by its corresponding place value.
259 written in expanded form:
2 x 100 + 5 x 10 + 9 x 1 = 200 + 50 + 9
Example 2: Write the number 15,057 in expanded notation.
We can begin by placing 15,057 into the place value chart; this will give us the place value for each digit in the number.

• 1 - Ten Thousands
• 5 - Thousands
• 0 - Hundreds
• 5 - Tens
• 7 - Ones

Now that we know the place values, we can write the number in expanded form. Again form the sum of each digit multiplied by its corresponding place value.
15,057 written in expanded form:
1 x 10,000 + 5 x 1000 + 0 x 100 + 5 x 10 + 7 x 1 = 10,000 + 5000 + 50 + 7
We can easily obtain the same result without a place value chart. In the place value lesson, we learned the rightmost digit of a number is in the ones' place. As we move left, we multiply by 10 to obtain the new place value.

• 1 - Ones
• 1 x 10 = 10 » Tens
• 10 x 10 = 100 » Hundreds
• 100 x 10 = 1000 » Thousands
• 1000 x 10 = 10,000 » Ten Thousands
• 10,000 x 10 = 100,000 » Hundred Thousands
• 100,000 x 10 = 1,000,000 » Millions

Example 3: Write the number 195,003 in expanded notation without using a place value chart.

• 1 - Hundred Thousands
• 9 - Ten Thousands
• 5 - Thousands
• 0 - Hundreds
• 0 - Tens
• 3 - Ones

Now that we know the place values, we can write the number in expanded form. Again form the sum of each digit multiplied by its corresponding place value.
195,003 written in expanded form:
1 x 100,000 + 9 x 10,000 + 5 x 1000 + 0 x 100 + 0 x 10 + 3 x 1 = 100,000 + 90,000 + 5000 + 3