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How to Write Numbers in Expanded Form

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  • 0:04 Expanded Form
  • 1:11 More Practice
  • 3:05 Lesson Summary
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Lesson Transcript
Instructor: Sarah Palacios

Sarah has completed her master’s degree in Education from the University of Texas and has received her bachelors in Interdisciplinary Studies specializing in Mathematics. She graduated with honors, Magna cum Laude, from Texas A&M University. She currently holds a principal certificate, a teaching certificate for Mathematics grades 4-8, a teaching certificate for EC – 6 as a generalist, as well as an ESL certificate. She has been an elementary school teacher for the past 4 years and is passionate about educating students to the highest degree.

Have you ever thought about how numbers are said and written? In this lesson, we will learn how to write numbers in expanded form so that you understand the value of each digit within the number.

Expanded Form

When writing numbers in expanded form, we've got to remember that it simply means to extend the digits out according to their place value. Knowing a number's place value helps us to understand the true value of each digit within a number.

Let's look at a chart showing numbers in their place value to the thousands:


Hundreds Chart321


The value of a number depends on its place. Let's look at an example with 7,692. Check out the chart on your screen now.


Hundreds Chart with Numbers


We can see the following:

  • The value of 7 is written as 7,000 because it's in the thousands place.
  • The value of 6 is written as 600 because it's in the hundreds place.
  • The value of 9 is written as 90 because it's in the tens place.
  • The value of 2 is written as 2 because it's in the ones place.

We can extend this out using expanded form by adding each number together to find the sum:

7,000 + 600 + 90 + 2 = 7,692

Now we understand the value of each digit within the number.

More Practice

Let's use base ten blocks to help us see this concept better:


Base Ten Blocks


Remember, the value of a cube is 1000, which is 1000 single unit blocks. The value of a flat is 100, which is 100 single unit blocks. The value of a rod is 10, which is 10 single unit blocks. The value of a unit is 1, or 1 single unit block. Using the same number that we used in our opening example, 7,692, let's find the value of each digit using base ten blocks.

  • The value of 7 is 7,000 because it's in the thousands place. This means there are 7 thousands, or 7 cubes.
  • The value of 6 is 600 because it's in the hundreds place. This means 6 hundreds, or 6 flats.
  • The value of 9 is 90 because it's in the tens place. This means 9 tens, or 9 rods.
  • The value of 2 is 2 because it is in the ones place. This means 2 units.

We find the sum of these values by adding them together:

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