Math 5Place Value in a Base 10

System

Instructor: Mrs. Tew Turner

In this lesson we will learn about place value for the

base 10 system.

Math Warm-upComplete the Table. Use mental math.

CostChange from

$10

$4.99

$6.75

$7.95

$9.10

$5.01

$3.25

$2.05

$0.90

Vocabulary

digit – a symbol used to make numerals (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

numerals – a symbol or name that stands for a number (3, 196, and twelve are all numerals)

Vocabulary

place – the position of a digit in a number

Ex. 486 The numeral 4 is in the hundreds place.

Vocabulary

value – product of a digit multiplied by its place (what it is worth)

Ex. 486 The numeral 4 represents 4 hundreds. Its value is four hundred.

Vocabulary

base 10 – a number system that is made from patterns of tens

How can you read and write large numbers?

Let’s use this number as an example:

3, 638, 241

Say:

“three million, six hundred thirty-eight thousand, two hundred forty-one”

3, 638, 241

Expanded:

3,000,000 + 600,000 + 30,000 + 8,000 + 200 + 40 + 1

3, 638, 241

Write:

3, 638, 241

3, 638, 241

Let’s practice doing that together for another number.2,459,038

Say: “two million, four hundred fifty-nine thousand, thirty-eight.

Expand: 2,000,000+400,000+50,000+9,000+30+8

Write: 2,459,038

Now it’s your turn.

1. 7,387,246 Say: Expand:

2. 3,250,997 Say: Expand:

3. 7,382,034 Say:

Expand:

How did you do?

1. 7,387,246

Say: seven million, three hundred eighty-seven, two hundred forty-six

Expand: 7,000,000+300,000+80,000+7,000+200+40+6

How did you do?

2. 3,250,997

Say: three million, two hundred fifty thousand, nine hundred ninety-seven

Expand: 3,000,000 + 200,000 + 50,000 + 900 + 90 + 7

How did you do?

3. 7,382,034

Say: seven million, three hundred eighty-two thousand, thirty-four

Expand: 7,000,000 + 300,000 + 2,000 + 30 + 4

Millions ,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

What is this chart called?

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

Place Value Chart

Millions ,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

Notice the comma’s name?

this is a column

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

What do the columns represent?

this is a column

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

Each column represents a different number value.

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

Make a chart like this in your notebook:

Why would we use a place value chart?

We would use a place value chart to help us understand numbers.

For example, I may ask you, “What is the place of the digit 4 in 3,467?”

You may use the place value chart to help you answer the question.

You would write the number in the place value chart starting with the number at the right. You would write that number in the ones column.

Let’s do that together to figure out the answer.

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

3, 4 6 7

What is the place of the digit 4 in 3,467?

Here is another example I may ask you, “What is the value of the digit 9 in 9,638?”

You may use the place value chart to help you answer the question.

You would write the number in the place value chart starting with the number at the right. You would write that number in the ones column.

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

9, 6 3 8

We wrote the number in the chart and discovered that the digit 9 is in the thousands column, or the thousands place.

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

9, 6 3 8

We know the place of the digit, but what is its value?

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

9, 6 3 8

We know there are nine in the thousands column, so 9,000 is the value.

I like to think of the value of a digit as what the digit is worth.

For example, in the United States of America, the money is measured in dollars. So, if I have 5 ten dollar bills, the worth of the digit 5 is 50 because I would have $50.00(fifty dollars).

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

2, 4 5 3, 9 7 2

Let’s find the value of the digit 5 in 2,453,972.First, write the number in the number chart.

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

2, 4 5 3, 9 7 2

Next, look for the digit 5 on the chart and find the place column of that digit.

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

2, 4 5 3, 9 7 2

Now, find the value of the digit.5 ten thousands = 50,000Think: (10,000+10,000+10,000+10,000+10,000)

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

Let’s find the value of the digit 2 in 275,968.

What is the first step?

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

2 7 5, 9 6 8

Now what do we do?

Millions,

Hundred Thousands

Ten Thousands

Thousands,

Hundreds

Tens Ones

2 7 5, 9 6 8

What is the last step?

What place is digit 8 in 9,345,841?What value is digit 8 in that number?

What place is digit 6 in 561,428?What is the value of digit 6 in that number?

What place is digit 3 in 3,925,976?What is the value of digit 3 in that number?

What place is digit 8 in 9,345,841?hundredsWhat value is digit 8 in that number?800What place is digit 6 in 561,428?Ten thousandsWhat is the value of digit 6 in that number?60,000What place is digit 3 in 3,925,976?millionsWhat is the value of digit 3 in that number?3,000,000

Quick Check

Write the number in standard form:1. Six million, two hundred thousand,

six2. 8,000,000 + 300 + 90 + 4

Write the number in expanded form:3. 7,204,6304. 1,298,004

In your Math Notebook

Quick Check

What is the value of the underlined digit in each number?

5. 48,9216. 7,587,092How does each 7 have a different value? Explain your thinking.

Today you learned how read, write, and say whole numbers to the millions!

Good Work with this

lesson.