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**Decimals and the Area Model**

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**Decimals are fractions written in a different form**

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

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

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**How many of these long bars fit in our grid?**

10

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

or

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

How can we write this as a fraction?

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.1 + .1 + .1 = .3 or = 𝟑 𝟏𝟎

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**What fraction of the whole is shaded?**

How do we represent this as a decimal?

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There are 10 columns

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and there are 10 rows..

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

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

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

How do we write this as a fraction?

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.2 + .05 = .𝟐𝟓

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

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**Is there another way to write the fraction 25 100 ?**

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

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**…so we can write the fraction**

= 1 4 Therefore .25 = = 1 4

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**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

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**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.

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

or

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

How can we write this as a fraction?

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

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**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.

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

or

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0.1 0.01 0.001 0.0001

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**What decimal number is represented by the shaded area?**

0.1 0.02 + 0.005 0.125

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**What decimal number is represented by the shaded area?**

0.2 0.05 0.007 + 0.0003 0.2573

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**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

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**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

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**Use the decimal grid to convert**

to decimal notation

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**Use the decimal grid to convert**

to decimal notation

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**Use a grid to convert the following fractions into decimal notation**

3 4 5 8 7 20

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