What is Expanded Notation? - Definition & Examples

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  • 0:01 What Is Expanded Notation?
  • 0:47 Using a Number Line
  • 3:28 Expanded to Standard
  • 4:45 Lesson Summary
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Lesson Transcript
Instructor: Kimberly Osborn
In this lesson, you'll learn how numbers can be expressed in three different ways, with an emphasis on expanded notation. You'll also find out how to convert numbers from the familiar standard form to expanded form and back again.

What Is Expanded Notation?

Did you know that numbers can be expressed in three different ways, two of which we use on an everyday basis? When you express a number in numerical digits, such as 1,947, you are using standard notation. We can also express this same number in written, or word form: one thousand nine hundred forty-seven. It is important to note that when working with numbers in word form, we do not use 'and' unless we are expressing a decimal point.

Expanded notation is a combination of both standard and word form. When we write a number in expanded notation, we break down each single digit to create a string of digits. Let's look at a number line to see exactly how we go about putting a number in expanded form.

Using a Number Line

Let's look at the number line to review our place values. Each specific spot on a number line is described using the value of that number. Remember, everything to the right of the number line ends in '-ths', like 'tenths,' 'hundredths,' etc.

Number Line

Using our earlier example of 1,947, we see that 1 is in the thousands place, 9 is in the hundreds place, 4 is in the tens place and 7 is in the ones place. Now, let's rewrite our number line using the numerical form for each place. This is going to make it very easy for us to see exactly how to write a number in expanded form.

Numerical Number Line

To convert a number from standard to expanded notation, we must first break apart each digit of our number, in this case: 1,947. Working our way from left to right on the number line, we see that 1 is in the thousands place, which we express as 1 x 1,000. Moving on to the next digit, we see that 9 is located in the hundreds place, so we write 9 x 100. The next digit, 4, is located in the tens place, which we express as 4 x 10. Our final digit, 7, is located in the ones place. We can either write this as 7 x 1, or just leave it as 7.

To express 1,947 in expanded notation, we insert a plus sign between each segment:

(1 x 1000) + (9 x 100) + (4 x 10) + (7)

We could also say: 1,000 + 900 + 40 + 7, which gives us 1,947, our original number expressed in standard form.

Now, let's try converting a number that includes a decimal, 360.52, to expanded notation. Again, working from left to right, we see that 3 is in the hundreds place, 6 is in the tens place and 0 is in the ones place. On the other side of the decimal, we see that 5 is in the tenths place, and 2 is in the hundredths place. Using our number line, we can expand each of these digits. In this case, our solution is:

(3 x 100) + (6 x 10) + (0) + (5 x 0.1) + (2 x 0.01)

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