MODELING DECIMALS WORKSHEET

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

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

3. Model 0.53 by shading a 10-by-10 grid.

4. Model 1.07 by shading a 10-by-10 grid.

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

6. The shaded parts of the models below each represents a fraction.

What is the sum of the fractions ?

A)  45/110      B)  65/110    C)  70/100     D)  72/100

7.  Jake used 1 centimeters cube to build a right rectangular prism that has the volume of 24 cubic centimeters. Which figure represent the prism that Jake built ?

8. Which expression could be represented by the shaded parts of the model below ?

A)  5/8 + 5/5     B)  5/8 x 5/5     C)  5/8 + 5

D)  5/8 x 5

9. A section of rectangular floor is covered with square tiles, as shown below. Each square tile has a side length of 1/3 foot.

What is the area, in square feet, the section of rectangular floor that is covered with floor tiles ?

1. Answer :

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

0.78 = 78/100

0.78 = 78%

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.

2. Answer :

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.

In 1.42 = 1 42/100 or 1 + 42/100, there are two parts.

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.

3. Answer :

Since there are two digits after the decimal point in 0.53, we can write 0.53 as a fraction 53/100.

0.53 = 53/100 = 53%

0.53 = 53 out of a hundred

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

Because 10 x 10  = 100.

Since 0.53  =  53 out of a hundred, we have to shade 53 out 100 parts in 10 by- 10 grid to model the decimal 0.53.

That is,

4. Answer :

There are two digits after the decimal point in 1.07. So, we can write 1.07 as a fraction 107/100.

Here, the numerator 107 is greater than 100.

Since we are going to use 10 by 10- grid (100 equal parts), we can write the given decimal 1.07 as given below.

1.07 = 1 + 0.07

1.07 = 100/100 + 7/100 = 1 7/100

In 1.07 = 1 7/100 or 1 + 7/100, there are two parts.

They are 1 and 7/100.

So, we have to use two 10 by-10 grids to model the decimal 1.07.

Since we write 1.07  =  100/100 + 7/100, we have to shade all the 100 parts in the first grid and 7 parts in the second grid.

5. Answer :

Percent means per hundred.

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% = 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.

6. Answer :

To find sum of fractions, we have to represent the fractions form of the shaded grids.

= 42/100 + 3/10

= 42/100 + (3/10) x (10/10)

= 42/100 + 30/100

= (42 + 30)/100

= 72/100

So, option D is correct.

7. Answer :

Given that volume of the rectangular prism = 24 cubic inches

Volume of rectangular prism = length x width x height

From option A, length = 3, width = 3 and height = 2

Volume = 3 x 3 x 2

= 18 cubic inches, so option A is not correct.

From option C, length = 8, width = 6 and height = 8

Volume = 8 x 6 x 8

= 384 cubic inches, so option C is not correct.

From option B, length = 12, width = 2 and height = 1

Volume = 12 x 2 x 1

= 24 cubic inches, so option B is correct.

8. Answer :

In each circle, we have 5 equal portions are shaded out of 8. So, fractional representation of each circle is 5/8.

= 5/8 + 5/8 + 5/8 + 5/8 + 5/8

= 5 x 5/8

So, otpion D is corect.

9. Answer :

Area of one square tile = 1/3 x 1/3

= 1/9

Number of square tiles = 20

Required area = 20 x 1/9

= 20/9 square foot.

Kindly mail your feedback to v4formath@gmail.com

We always appreciate your feedback.