What is Expanded Form in Math? - Definition & Examples

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  • 0:00 Place Value
  • 0:55 Expanded Form
  • 3:12 Expanded Form to Standard Form
  • 3:37 Lesson Summary
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Lesson Transcript
Instructor: Joseph Vigil
In this lesson, we'll review place value and find out how it's useful when writing numbers in expanded form. We'll also look at a few examples of numbers written out in expanded form.

Place Value

What makes a number mean what it does? Is it simply the digits in the number? For example, let's consider the number 521.

If we switch the digits around, we might get 125. Definitely not the same number. So, it's not just the digits that make a number; it's the digits and their positions within the number. A digit's position in a number and its resulting value is called place value.

The place value chart for our number system looks like this:

Place Value Chart to the Millions Place
Place Value Chart to the Millions Place

If we place our original number, 521, into this chart, it now looks like this:

521 in a Place Value Chart
521 in a Place Value Chart

Since the digit 5 is in the hundreds place, it means that we have five hundreds, or 500, of whatever we're talking about. Since the two is in the tens place, it means two tens, or 20. And since one is in the ones place, it means one one, or 1.

Expanded Form

When we write the number 521, what that number really means is that we have the total of 500 + 20 + 1. We've expanded the number to show the value of each of its digits. When we expand a number to show the value of each digit, we're writing that number in expanded form.

Let's try it with a different, bigger number: 1,234,567. We'll start by placing the number's digits in the place value chart.

Place Values of 1,234,567
Place Values of 1,234,567

Now, let's use the chart to determine the value of each digit.

  • Since the 1 is in the millions place, it means one million, or 1,000,000
  • Since the 2 is in the hundred thousands place, it means two hundred thousands, or 200,000
  • Since the 3 is in the ten thousands place, it means three ten thousands, or 30,000
  • Since the 4 is in the thousands place, it means four thousands, or 4,000
  • Since the 5 is in the hundreds place, it means five hundreds, or 500
  • Since the 6 is in the tens place, it means six tens, or 60
  • Since the 7 is in the ones place, it means seven ones, or 7

If we write the number out in expanded form, showing the value of each digit, we would write it as 1,000,000 + 200,000 + 30,000 + 4,000 + 500 + 60 + 7. And that's all there is to it!

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