Decimals and the Area Model

Decimals are fractions written in a different form 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 1 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… or

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 10 + 1 10 + 1 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 … …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?

.2 + .05 = .𝟐𝟓

…and as a fraction – 25 100 Since 25 out of 100 boxes are shaded

Is there another way to write the fraction 25 100 ?

1 3 2 4 How many of these fit in the whole unit?

…so we can write the fraction 25 100 = 1 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

100 10 How many of these little bars fit across the top of our grid? 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… or

Your turn – shade a portion of the whole that represents .004 How can we write this as a fraction?

.001 + .001 + .001 + .001 = .004

100 100 How many little squares fit across the top of our grid? 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… or

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

Let’s start with the fraction Now for the very cool application of the decimal grid to the conversion of fractions into decimal notation Let’s start with the fraction

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

Use the decimal grid to convert to decimal notation

Use the decimal grid to convert to decimal notation

Use a grid to convert the following fractions into decimal notation 3 4 5 8 7 20