1. Decimals and the Area Model

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

3. For example how do we shade a portion of the grid that represents 1 10 ?

4. How many of these long bars fit in our grid?10

5. Since there are 10 of the long bars in the entire unit grid, each bar represents…or

6. Your turn – Shade a part of the whole that is represented by the decimal .3
How can we write this as a fraction?

7. .1
+ .1
+ .1
= .3 or
= 𝟑 𝟏𝟎

8. What fraction of the whole is shaded?
How do we represent this as a decimal?

9. There are 10 columns

10. and there are 10 rows..

11. So, in the entire grid, there are 10 x 10 = 100 medium squares.

12. So, the fraction is …
…and as a decimal …

13. Your turn – shade a part of the whole that is represented by .25
How do we write this as a fraction?

14. .2
+ .05
= .𝟐𝟓

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

16. Is there another way to write the fraction 25 100 ?

17. 1 3 2 4
How many of these fit in the whole unit?

18. …so we can write the fraction
= 1 4
Therefore
.25 = = 1 4

19. There are many ways to write the portion of a whole with fractions…
= 1 4 =
But, only one way to write that portion as a decimal
.25

20. 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.

21. Since there are 1000 of the little bars in the entire unit grid, each bar represents…or

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

23. .001 +
.001 +
.001 +
.001
= .004

24. 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 x 100 = little squares in the entire grid.

25. Since there are 10000 of the little squares in the entire unit grid, each square represents…or

26. 0.1
0.01
0.001
0.0001

27. What decimal number is represented by the shaded area?
0.1
0.02 +
0.005
0.125

28. What decimal number is represented by the shaded area?
0.2
0.05
0.007 +
0.0003
0.2573

29. 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

30. 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

31. Use the decimal grid to convert
to decimal notation

32. Use the decimal grid to convert
to decimal notation

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