Lesson Objectives

- Demonstrate an understanding of place value
- Understand the definition of expanded form
- Learn how to write a number in expanded form using a place value chart
- Learn how to write a number in expanded form without a place value chart

## How to Write a Number in Expanded Form?

In the last lesson, we covered the topic of Place Value. We learned how to set up a place value chart, which helps to identify the place of each digit in a given number. When we dig further into the topic of place value, we learn that we can write a number in a manner that shows the value of each digit. This method is known as expanded form or expanded notation. To write a number in expanded form, simply form the sum of each digit multiplied by its corresponding place value. Let's use our place value chart and look at a few examples.

Example 1: Write the number 259 in expanded notation.

We can begin by placing 259 into the place value chart; this will give us the place value for each digit in the number.

259 written in expanded form:

2 x 100 + 5 x 10 + 9 x 1 = 200 + 50 + 9

Example 2: Write the number 15,057 in expanded notation.

We can begin by placing 15,057 into the place value chart; this will give us the place value for each digit in the number.

15,057 written in expanded form:

1 x 10,000 + 5 x 1000 + 0 x 100 + 5 x 10 + 7 x 1 = 10,000 + 5000 + 50 + 7

We can easily obtain the same result without a place value chart. In the place value lesson, we learned the rightmost digit of a number is in the ones' place. As we move left, we multiply by 10 to obtain the new place value.

195,003 written in expanded form:

1 x 100,000 + 9 x 10,000 + 5 x 1000 + 0 x 100 + 0 x 10 + 3 x 1 = 100,000 + 90,000 + 5000 + 3

Example 1: Write the number 259 in expanded notation.

We can begin by placing 259 into the place value chart; this will give us the place value for each digit in the number.

- 2 - Hundreds
- 5 - Tens
- 9 - Ones

259 written in expanded form:

2 x 100 + 5 x 10 + 9 x 1 = 200 + 50 + 9

Example 2: Write the number 15,057 in expanded notation.

We can begin by placing 15,057 into the place value chart; this will give us the place value for each digit in the number.

- 1 - Ten Thousands
- 5 - Thousands
- 0 - Hundreds
- 5 - Tens
- 7 - Ones

15,057 written in expanded form:

1 x 10,000 + 5 x 1000 + 0 x 100 + 5 x 10 + 7 x 1 = 10,000 + 5000 + 50 + 7

We can easily obtain the same result without a place value chart. In the place value lesson, we learned the rightmost digit of a number is in the ones' place. As we move left, we multiply by 10 to obtain the new place value.

- 1 - Ones
- 1 x 10 = 10 » Tens
- 10 x 10 = 100 » Hundreds
- 100 x 10 = 1000 » Thousands
- 1000 x 10 = 10,000 » Ten Thousands
- 10,000 x 10 = 100,000 » Hundred Thousands
- 100,000 x 10 = 1,000,000 » Millions

- 1 - Hundred Thousands
- 9 - Ten Thousands
- 5 - Thousands
- 0 - Hundreds
- 0 - Tens
- 3 - Ones

195,003 written in expanded form:

1 x 100,000 + 9 x 10,000 + 5 x 1000 + 0 x 100 + 0 x 10 + 3 x 1 = 100,000 + 90,000 + 5000 + 3

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