Lesson Objectives
  • Understand the definition of expanded form
  • Learn how to write a number in expanded form using a place value chart
  • Learn how to write a number in expanded form without a place value chart

How to Write a Number in Expanded Form?


In the last lesson, we covered the topic of Place Value. We learned how to setup a place value chart, which helps to identify the place of each digit in a given number. place value chart 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. place value chart
  • 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. place value chart
  • 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 right most digit of a number is in the one's place. As we move left, we multiply the previous place value 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.
A number draw with its place value of each digit shown above
  • 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