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
1
represents ?
10
How many of
these long bars
fit in our grid?
10
Since there are
10 of the long
bars in the entire
unit grid, each
bar represents…
1
10
or
.1
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
1
1
1
+
+
10 10 10
=
𝟑
𝟏𝟎
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.
So, the
fraction is …
1
100
…and as a
decimal …
.01
Your turn –
shade a part
of the whole
that is
represented
by .25
How do we
write this as
a fraction?
.2
+ .05
= . 𝟐𝟓
…and as a
fraction –
25
100
Since 25 out
of 100 boxes
are shaded
Is there another
way to write the
25
fraction
?
100
How many of
these fit in
the whole
unit?
4
3
1
2
…so we can
write the
fraction
25
1
=
100 4
Therefore
.25 =
25
100
=
1
4
There are many ways to write the
portion of a whole with fractions…
25
100
1
=4=
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?
0.1
0.02
+ 0.005
0.125
What decimal
number is
represented by
the shaded area?
0.2
0.05
0.007
+ 0.0003
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
4
This can be read
as 1 part out of
every 4
So, out of these
4 bars, we can
shade 1
And out of these
4 bars, we can
shade 1
Out of these 4
squares, we
can shade 1
And so forth…
Until we have
used up all of the
original unit
1
 0.25
4
Use the
decimal grid
to convert
3
8
to decimal
notation
.3
.06
.015
.375

Use the
decimal grid
to convert
1
3
to decimal
notation
.3
.03
.003
.0003
.
.
.
.3333...
1
 .3
3
Use a grid to
convert the
following fractions
into decimal
notation
3
4
5
8
7
20