LESSON: Decimal Place Value

INTRODUCTION

READ: Express Numbers Given in Words or Hundredths Grids Using Decimal Place Value

Express Numbers Given in Words or Hundredths Grids Using Decimal Place Value

A whole number represents a whole quantity. There aren’t any parts when we work with a whole number.When we have a part of a whole, we can write it in a couple of different ways. One of the ways that we write it is as a decimal. A decimal is a part of a whole.

Example

4.56

This decimal has parts and wholes in it. Notice that there is a point in the middle of the number. This is called the decimal point. The decimal point helps us to divide the number between wholes and parts. To the right of the decimal point is the parts of the whole and to the left of the decimal point is the whole number.

We can have numbers with parts and wholes in them, and we can have numbers that are just decimals.

Example

.43

This decimal has two decimal places. Each digit after the decimal is in a different place. We call these places place value. When you were working with whole numbers you used place value too, but this is a new place value system that includes decimals.

How can we express a decimal using place value? To express a decimal using place value we need to use a place value chart. This gives us an idea about the worth of the decimal.

Here is a place value chart.

Notice that if we take the last example and write it in the place value chart above each number is a word. That word gives us the value of that digit according to its place in the chart. This number is forty-three hundredths. The three is in the hundredths place so that lets us know that this is hundredths.

What whole is this decimal a part of?

To better understand what whole the decimal is a part of, we can use a picture. We call these grids or hundreds grids. Notice that the number in the last example was .43 or 43 hundredths. The hundredths lets us know that this is “out of one hundred.”

Here is a picture of a hundreds grid.

Now we want to show 43 hundredths of the hundreds grid. To do that, we shade 43 squares. Each square is one part of one hundred.

What about tenths?

If you look at a place value chart, you can see that there are other decimal names besides hundredths. We can also have tenths.

Example

.5

Here is a number that is five-tenths. We can create a picture of five-tenths using a grid of ten units.

If we want to show .5 in this box, we can see that tenths means 5 out of 10. We shade five boxes of the ten.

WATCH: Model Decimals

READ: Express Decimals in Expanded Form

Express Numbers in Expanded Form Given Decimal Form

Expanded form is when a number is stretched out. Let’s look at a whole number first and then use this information with decimals.

Example

265

If we read this number we can read it as two hundred and sixty-five. We can break apart this to say that we have two hundreds, six tens and five ones. Let’s look at our place value chart to help us make sense of it.

The two is in the hundreds place. The six is in the tens place and the five is in the ones place.

Here it is in expanded form: 2 hundreds + 6 tens + 5 ones

This uses words, how can we write this as a number?

200 + 60 + 5

Think about this, two hundred is easy to understand. Six tens is sixty because six times 10 is sixty. Five ones are just that, five ones. This is our number in expanded form.

How can we write decimals in expanded form?

We can work on decimals in expanded form in the same way. First, we can look at a decimal and put it into a place value chart to learn the value of each digit.

Example

.483

Now we can see the value of each digit.

4 = four tenths

8 = eight hundredths

3 = 3 thousandths

We have the value in words, now we need to write them as numbers.

Four tenths = .4

Eight hundredths = .08

Three thousandths = .003

What are the zeros doing in there when they aren’t in the original number? The zeros are needed to help us mark each place. We are writing a number the long way, so we need the zeros to make sure that the digit has the correct value. If we didn’t put the zeros in there, then .8 wouldn’t be 8 hundredths it would be 8 tenths.

Now, we can write this out in expanded form.

.483

.4 + .08 + .003 = .483

This is our answer in expanded form.

READ: Decimals to Ten-Thousandths Place

Read and Write Decimals to Ten-Thousandths Place

How do we read a decimal? We read a decimal by using the words that show the place value of the last digit of the decimal. That may sound confusing, so let’s look at an example.

Example

.45

To help us read this decimal, we can put it into our place value chart.

We can read this decimal by using the place value of the last digit to the right of the decimal point. Normally, we would read this number as forty-five. Because it is a decimal, we read it with the place value of the last digit to the right of the decimal point. We read forty-five hundredths. The last digit is a five and it is in the hundredths place.

Can we use place value to write the number too? Yes we can. We write the number as we normally would.

Example

Forty-five

Next, we add the place value of the last digit to the right of the decimal point.

Forty-five hundredths

Our answer is forty-five hundredths.

We can use this method to read and write any decimal. What about a decimal with more digits?

Example

.5421

First, let’s put this number in our place value chart.

First, let’s read the number.We can look at the number without the decimal. It would read:

Five thousand four hundred twenty-one

Next we add the place value of the last digit

Ten thousandth

Five thousand four hundred and twenty-one ten thousandths

This is our answer.

It is also the way we write the number in words too. Notice that is it very important that we add the THS to the end of the place value when working with decimals

EXAMPLE 1

Decimal Place Value

EXAMPLE 2

Decimal Place Value Part 2

CHECK Yourself! Decimals