Contributed by:

In this pdf we will discuss about decimals. A decimal may have both a whole-number part and a fractional part. The whole-number part of a decimal are those digits to the left of the decimal point. The fractional part of a decimal is represented by the digits to the right of the decimal point.

1.
What is a

2.
What is a decimal?

A decimal is similar to a fraction –

It’s not a whole number.

Rather than saying ½, we can say 0.50

Instead of writing 1/10, we can say

one-tenth or 0.1.

It’s simply another form of a fraction.

A decimal is similar to a fraction –

It’s not a whole number.

Rather than saying ½, we can say 0.50

Instead of writing 1/10, we can say

one-tenth or 0.1.

It’s simply another form of a fraction.

3.
What is a decimal?

A decimal is a part of a number. We use

decimals most often when we are talking

about money.

$13.45

How would you read this number?

A decimal is a part of a number. We use

decimals most often when we are talking

about money.

$13.45

How would you read this number?

4.
$13.45

Thirteen dollars and forty five cents.

Remember:

You do not need to use the ¢ when your

money amount is greater than $1.

Thirteen dollars and forty five cents.

Remember:

You do not need to use the ¢ when your

money amount is greater than $1.

5.
What does the .45 mean?

.45 is the same thing as saying 45¢ .

It means that it is only a part of a dollar.

It is not the whole dollar.

.45 is the same thing as saying 45¢ .

It means that it is only a part of a dollar.

It is not the whole dollar.

6.
Why do I have to understand

decimals?

This is a good question.

We need to understand what the value of

each number means in order to

understand what we are talking about.

Here is an example:

A shirt costs $12.05, but when I wrote the

number down I wrote $12.5.

What’s wrong with this?

decimals?

This is a good question.

We need to understand what the value of

each number means in order to

understand what we are talking about.

Here is an example:

A shirt costs $12.05, but when I wrote the

number down I wrote $12.5.

What’s wrong with this?

7.
Why is $12.5 wrong?

$12.5 really is saying $12.50, because when we

read how much something costs it always has

two places after the decimal point.

If we don’t have a digit after the first number we

must assume it is a zero. However, when we

read $12.05, the zero is the place holder so we

know it is 5¢ and not 50¢. That is a 45¢

difference. I can get a piece of gum for that

amount!

$12.5 really is saying $12.50, because when we

read how much something costs it always has

two places after the decimal point.

If we don’t have a digit after the first number we

must assume it is a zero. However, when we

read $12.05, the zero is the place holder so we

know it is 5¢ and not 50¢. That is a 45¢

difference. I can get a piece of gum for that

amount!

8.
Let’s Look at Some Place Value

One Ten One Ten Cents

Hundred Dollars Dollar Cents

1 3 7 8 2

Hundreds Tens Ones Tenths Hundredths

1 3 7 8 2

AND

One Ten One Ten Cents

Hundred Dollars Dollar Cents

1 3 7 8 2

Hundreds Tens Ones Tenths Hundredths

1 3 7 8 2

AND

9.
How do I read a decimal?

If you look at the number 12.3, you say:

Twelve and three tenths.

If you look at the number 12.35, you say:

Twelve and thirty-five hundredths.

If you look at a number 12.05, you say:

Twelve and five hundredths.

Now you practice saying them!

If you look at the number 12.3, you say:

Twelve and three tenths.

If you look at the number 12.35, you say:

Twelve and thirty-five hundredths.

If you look at a number 12.05, you say:

Twelve and five hundredths.

Now you practice saying them!

10.
Let’s Write these Numbers in

Expanded Form

If we are using money, it would look

like this:

$100 + $30 + $7 + 80¢ + 2¢ = $137.82

If we are using decimals, it would

look like this:

100 + 30 + 7 + .8 + .02 = 137.82

Expanded Form

If we are using money, it would look

like this:

$100 + $30 + $7 + 80¢ + 2¢ = $137.82

If we are using decimals, it would

look like this:

100 + 30 + 7 + .8 + .02 = 137.82

11.
How do I Compare and Order

decimals?

7.3 and 7.03 – Which is larger?

ORGANIZE – Write the numbers vertically by lining up the decimal

points.

7.3

7.03

EQUALIZE – Add a zero to make the numbers all have the same

number of digits

7.30

7.03

ORDER – Start with the largest place and compare the decimals.

7.30 > 7.03

decimals?

7.3 and 7.03 – Which is larger?

ORGANIZE – Write the numbers vertically by lining up the decimal

points.

7.3

7.03

EQUALIZE – Add a zero to make the numbers all have the same

number of digits

7.30

7.03

ORDER – Start with the largest place and compare the decimals.

7.30 > 7.03

12.
Compare and Order –

Another Example

Order from least to greatest: 12.34; 12.4; 12.43; 12.3

ORGANIZE – Write the numbers vertically by lining up the decimal points.

12.34

12.4

12.43

12.3

EQUALIZE – Add a zero to make the numbers all have the same number of digits

12.34

12.40

12.43

12.30

ORDER – Start with the largest place and write the decimals in order.

12.30; 12.34; 12.40; 12.43

Another Example

Order from least to greatest: 12.34; 12.4; 12.43; 12.3

ORGANIZE – Write the numbers vertically by lining up the decimal points.

12.34

12.4

12.43

12.3

EQUALIZE – Add a zero to make the numbers all have the same number of digits

12.34

12.40

12.43

12.30

ORDER – Start with the largest place and write the decimals in order.

12.30; 12.34; 12.40; 12.43

13.
When else do we use decimals?

• Weight (He weighed 85.5 lbs)

• Temperature (It was so cold today, it was

only 43.7°)

• Measuring distances (example: the race

was a 5 kilometers or 3.1 miles long

• Can you think of any other times?

• Weight (He weighed 85.5 lbs)

• Temperature (It was so cold today, it was

only 43.7°)

• Measuring distances (example: the race

was a 5 kilometers or 3.1 miles long

• Can you think of any other times?