Lesson Objectives

- Learn about the whole numbers
- Learn how to create a place value chart
- Learn how to find the place value of a given digit in a number using a place value chart
- Learn how to find the place value of a given digit in a number without a place value chart

## What is Place Value?

When we begin learning basic arithmetic, our study involves the use of the group of numbers known as the whole numbers.

Whole Numbers: {0,1,2,3,4,5,...}

The whole numbers begin with a 0, and increase in increments of 1 indefinitely. There is no largest whole number. This is shown using an ellipsis or three dots "..." after the 5. This simply tells us that the pattern of increasing by 1 will continue forever. The numbers 0 through 9 have a special name, these numbers are referred to as the "digits".

Digits: {0,1,2,3,4,5,6,7,8,9}

Our number system relies on the digits along with place value to construct each number. Single-digit numbers are very easy to understand. The number 5, simply has one digit and its value is 5. When we look at multi-digit numbers, the situation is a bit more complex. In the number 53, the 5 no longer has a value of simply 5, it now represents a value of 50. To understand why we look to our place value system. Under the place value system, a digit obtains its value based on its position or placement in a number. Let's take a look at an example:

Observe how the value of the digit 8 changes in each number:

8 - The 8 means 8 ones, or just 8

83 - The 8 means 8 tens, or 80

859 - The 8 means 8 hundreds, or 800

8032 - The 8 means 8 thousands, or 8000

We can see from our example, that changing the position or placement of a digit, changes its value. Generally, we learn place value with a visual aid known as a place value chart: If we start at the rightmost position of the place value chart, we see it begins with the ones' place. As we move left, we are simply multiplying by ten to get to the next place. Moving to the left of the ones' place is the tens' place, since 1 x 10 = 10. Then we come across the hundreds' place (10 x 10 = 100). This pattern continues out indefinitely. We simply keep multiplying the previous place by ten to obtain the next place to the left.

Example 1: Write 759 in the place value chart, and give the place of each digit.

Example 3: Write 8,352,194 in the place value chart, and give the place of each digit.

Example 4: Give the place of each digit for the number 2509, without a place value chart.

Whole Numbers: {0,1,2,3,4,5,...}

The whole numbers begin with a 0, and increase in increments of 1 indefinitely. There is no largest whole number. This is shown using an ellipsis or three dots "..." after the 5. This simply tells us that the pattern of increasing by 1 will continue forever. The numbers 0 through 9 have a special name, these numbers are referred to as the "digits".

Digits: {0,1,2,3,4,5,6,7,8,9}

Our number system relies on the digits along with place value to construct each number. Single-digit numbers are very easy to understand. The number 5, simply has one digit and its value is 5. When we look at multi-digit numbers, the situation is a bit more complex. In the number 53, the 5 no longer has a value of simply 5, it now represents a value of 50. To understand why we look to our place value system. Under the place value system, a digit obtains its value based on its position or placement in a number. Let's take a look at an example:

Observe how the value of the digit 8 changes in each number:

8 - The 8 means 8 ones, or just 8

83 - The 8 means 8 tens, or 80

859 - The 8 means 8 hundreds, or 800

8032 - The 8 means 8 thousands, or 8000

We can see from our example, that changing the position or placement of a digit, changes its value. Generally, we learn place value with a visual aid known as a place value chart: If we start at the rightmost position of the place value chart, we see it begins with the ones' place. As we move left, we are simply multiplying by ten to get to the next place. Moving to the left of the ones' place is the tens' place, since 1 x 10 = 10. Then we come across the hundreds' place (10 x 10 = 100). This pattern continues out indefinitely. We simply keep multiplying the previous place by ten to obtain the next place to the left.

- 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

Example 1: Write 759 in the place value chart, and give the place of each digit.

- 7 - Hundreds
- 5 - Tens
- 9 - Ones

- 2 - Ten Thousands
- 6 - Thousands
- 0 - Hundreds
- 4 - Tens
- 1 - Ones

Example 3: Write 8,352,194 in the place value chart, and give the place of each digit.

- 8 - Millions
- 3 - Hundred Thousands
- 5 - Ten Thousands
- 2 - Thousands
- 1 - Hundreds
- 9 - Tens
- 4 - Ones

Example 4: Give the place of each digit for the number 2509, without a place value chart.

- 2 - Thousands
- 5 - Hundreds
- 0 - Tens
- 9 - Ones

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