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Math for Kids23 chapters | 325 lessons

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Lesson Transcript

Instructor:
*Sarah Palacios*

Sarah has completed her masterâ€™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 â€“ 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.

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:

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.

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.

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

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:

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

Let's look at a different number: 1,583. We'll look at each digit and find its place value.

- The 1 is in the thousands place so its value is 1,000. This equals 1 cube.
- The 5 is in the hundreds place so its value is 500. This equals 5 flats.
- The 8 is in the tens place so its value is 80. This equals 8 rods.
- The 3 is in the ones place so its value is 3. This equals 3 units.

Now we find the sum by adding these values together:

1,000 + 500 + 80 + 3 = 1,583

Let's take a few moments to recap what we've learned about writing numbers in **expanded form**. This is important because knowing how to write a number in expanded form helps us understand that each digit has its own value. Writing the number in expanded form means to write the value of each digit then add them together to find the sum. For example, the number 1,234 has the following values:

- The value of 1 is written as 1,000 because it's in the thousands place.
- The value of 2 is written as 200 because it's in the hundreds place.
- The value of 3 is written as 30 because it's in the tens place.
- The value of 4 is written as 4 because it's in the ones place.

Therefore, 1,000 + 200 + 30 + 4 = 1,234. Simple, right?

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Math for Kids23 chapters | 325 lessons

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