# MODELING DECIMAL FRACTION AND PERCENT EQUIVALENTS

Modeling Decimal Fraction and Percent Equivalents :

Using models can help us to understand how decimals, fractions, and percents are related.

In this section, we will learn, how to model the relations between decimals, fractions and percents.

## Modeling Decimal Fraction and Percent Equivalents - Examples

Example 1 :

Model 0.78 by shading a 10-by-10 grid.

Solution :

Since there are two digits after the decimal point in 0.78, we can write 0.78 as a fraction 78/100.

So, we have

0.78  =  78 / 100

0.78  =  78%

(or)

0.78  =  78 out of a hundred

In 10 by- 10 grid, there will be 100 equal parts.

Because 10 x 10  =  100.

Since 0.78  =  78 out of a hundred, we have to shade 78 out 100 parts in 10 by- 10 grid to model the decimal 0.78

That is, Example 2 :

Model 1.42 by shading a 10-by-10 grid.

Solution :

There are two digits after the decimal point in 1.42. So, we can write 1.42 as a fraction 142/100.

Here, the numerator 142 is greater than 100.

Since we are going to use 10 by 10- grid (100 equal parts), we can write the given decimal 1.42 as given below. 1.42 can be written as shown below.

1.42  =  1 42/100

1.42  =  1 + 42/100

Therefore, there are two parts in 1.42.

They are 1 and 42/100.

So, we have to use two 10 by-10 grids to model the decimal 1.42

Since we write 1.42  =  100/100 + 42/100, we have to shade all the 100 parts in the first grid and 42 parts in the second grid. Example 3 :

Model 125% by shading a 10-by-10 grid.

Solution :

Percent means per hundred.

So, we have

125%  =  125 / 100

Here, the numerator 125 is greater than 100.

Since we are going to use 10 by 10- grid (100 equal parts), we can write 125% as given below. 125% can be written as shown below.

125%  =  125 / 100

125%  =  1.25

125%  =  1 25/100

125%  =  1 + 25/100

Therefore, there are two parts in 125%.

They are 1 and 25/100.

So, we have to use two 10 by-10 grids to model 125%

Since we write 125%  =  100/100 + 25/100, we have to shade all the 100 parts in the first grid and 25 parts in the second grid.  After having gone through the stuff given above, we hope that the students would have understood, how to model equivalent percents, decimals and fractions.

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