Place Value: Expanded Form

Contributor: Meghan Vestal. Lesson ID: 11807

If you place a lot of value on writing numbers correctly, you'll need to learn how to simplify (4x1,000)+(3x0.001) and similar terms! Expand your knowledge with online games and a practice worksheet!


Integers/Rational Numbers and Operations

learning style
personality style
Lion, Beaver
Grade Level
Intermediate (3-5)
Lesson Type
Quick Query

Lesson Plan - Get It!

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  • What number is represented below?
  • Why would you write it this way?

400,000 + 80,000 + 8,000 + 60 + 3 + 0.4 + 0.02

  • Were you able to determine what number was represented above?

You may have been able to figure it out just by looking at it, or you may have had to add the numbers together on a piece of paper. Either way, you should have said this is equal to 488,063.42.

In the previous Related Lessons, found in the right-hand sidebar, you have learned how to read, write, and compare numbers expressed in standard and written form.

In this lesson, you will learn to read and write numbers expressed in expanded form. The number at the beginning of the lesson is written in expanded form.

  • What do you notice about the number written in expanded form?

Expanded form separates a number so each digit and its place value is displayed. Addition signs are placed between each part of the number, because if you add all the parts together, you will find the total value of the number.

Expanded form can be written one of two different ways. Each of the following examples shows the same number written in expanded form.

Compare and contrast the numbers. Then, determine what number the examples represent:

  • 40,000 + 9,000 + 20 + 8 + 0.03 + 0.003
  • (4 x 10,000) + (9 x 1,000) + (2 x 10) + (8 x 1) + (3 x 0.01) + (3 x 0.001)
  • Did you say each of the examples represents 49,028.033?
  • Which of the examples did you find easier to read?

When you are asked to write a number in expanded form, you can choose which method you prefer, but it is important to be able to read numbers using either method.

Expanded form is the form of writing a number that you are least likely to see in the real world, but it is still important to understand expanded form, because it teaches you how to break a number into parts.

When you understand all this, move on to the Got It? section to practice writing numbers in expanded form.

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