Lesson Objectives

- 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 setup 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 right most digit of a number is in the one's place. As we move left, we multiply the previous place value 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 right most digit of a number is in the one's place. As we move left, we multiply the previous place value 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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