Decimals and the Area Model

Decimals are fractions written in a different form. They represent a part of the whole

For example how do we shade a portion of the grid that represents ?

How many of these long bars fit in our grid?

10

1

10

or

.1

Since there are 10 of the long bars in the entire unit grid, each bar

represents…

Your turn – Shade a part of the whole that is represented by the decimal .3

How can we write this as a fraction?

.1 + .1 + .1

= .3

or=

What fraction of the whole is shaded?

How do we represent this as a decimal?

There are 10 columns

and there are 10 rows..

So, in the entire grid, there are 10 x 10 = 100

medium squares.

1

100

.01

So, the fraction is …

…and as a decimal …

Your turn – shade a part of the whole that is represented by .25

How do we write this as a fraction?

¿ .𝟐𝟓

.2+ .05

…and as a fraction –

Since 25 out of 100 boxes are shaded

Is there another way to write the

fraction ?

How many of these fit in the whole unit?

1 2

3 4

…so we can write the fraction

Therefore

.25 =

There are many ways to write the portion of a whole with fractions…

=

But, only one way to write that portion as a decimal

.25

How many of these little bars fit

across the top of our grid?

100

How many of these little bars fit down the side of our grid?

10

So, in the entire grid, there are 10 x 100 = 1000 little bars.

Since there are 1000 of the little bars in the entire unit

grid, each bar represents…

1

1000

or

.001

Your turn – shade a portion of the whole that represents .004

How can we write this as a fraction?

.001

+

.001

+

.001

+

.001

= .004

How many little squares fit across the top of our

grid?100

How many little squares fit down the side of our

grid?100

So there are 100 x 100 = 10000 little squares in the entire grid.

Since there are 10000 of the little

squares in the entire unit grid, each square

represents…1

10000

or

.0001

0.1

0.01

0.001

0.0001

What decimal number is

represented by the shaded

area?

0.125

+

0.1

0.02

0.005

What decimal number is

represented by the shaded

area?

0.2

0.05

0.0070.0003

0.2573

+

Now for the very cool

application of the decimal grid to the conversion of fractions into

decimal notation

Let’s start with the fraction

1

4

1

4This can be

read as 1 part out of every 4So, out of

these 4 bars, we can shade 1

And out of these 4 bars, we can shade 1Out of these 4 squares, we can shade

1And so forth…Until we have

used up all of the original

unit10.25

4

Use the decimal grid to convert

8

3

to decimal notation

.3

.06

.015

.375

Use the decimal grid to convert

to decimal notation

1

3

.3

.03

.003

1

3.3

.0003

.

.

.

.3333...

Use a grid to convert the following fractions into decimal notation

34

58

720