Converting Decimal Fractions to Simple Fractions and Mixed Numbers - Examples, Exercises and Solutions

To solve this problem, we will determine how much of the whole grid is represented by the shaded area.

The problem provides a 10x10 grid which contains 100 smaller squares in total. Our task is to determine how many of these squares are shaded.

Upon inspection, we count that 80 out of the 100 squares are shaded.

Therefore, the fraction of the whole that the shaded area represents is given by dividing the number of shaded squares by the total number of squares:

$\frac{\text{shaded squares}}{\text{total squares}} = \frac{8}{10}$

Converting this fraction to a decimal gives $0.8$.

Thus, the shaded area represents $\frac{8}{10}$ or $0.8$ of the whole.

Among the choices provided, the correct answer is: $0.8$ or $\frac{8}{10}$.

To solve this problem, we need to assess how much of the grid is shaded:

• Step 1: Notice that the grid is evenly divided into smaller, equal-sized squares.
• Step 2: Observe that every single section of the grid is shaded blue, with no portions left unshaded.
• Step 3: Consider that when an entire segment, like a grid, is covered entirely by shading, it represents the whole, which is equivalent to $1$ or the fraction $\frac{10}{10}$.

Therefore, since the whole grid is shaded, the shaded area represents $1$ or $\frac{10}{10}$ of the whole.

To solve this problem, let's follow these steps:

• Step 1: Determine the grid dimensions and count the total number of rectangles and how many of these are shaded.
• Step 2: Compute the fraction of the area that is shaded.
• Step 3: Convert this fraction to a decimal.

Now, let's work through each step:
Step 1: Upon examining the diagram, we see the whole is a 4x5 grid, hence
There are $4 \times 5 = 20$ rectangles in total.
The blue shaded area occupies the entire left-most column of this 4-column grid, so 4 rectangles are shaded.

Step 2: Calculate the fraction of the total area that is shaded:
The fraction of the shaded area is $\frac{\text{Number of Shaded Parts}}{\text{Total Number of Parts}} = \frac{4}{20}$.
Simplifying this gives $\frac{1}{5}$.

Step 3: Convert the fraction $\frac{1}{5}$ into a decimal:
Dividing 1 by 5 yields $0.2$.

The correct representation of the shaded area is indeed a part of the larger rectangle, showing that $\frac{4}{10}$ simplified to $\frac{2}{5}$ and thus represents $0.4$ in decimal form.

Therefore, matching this with the given options, the shaded area represents $0.4$ or $\frac{4}{10}$ of the entire area.

To solve this problem, we will determine the fraction of the grid that is shaded by following these steps:

• Step 1: Determine the Layout of the Grid.
  The grid is divided into $5 \times 10$ smaller squares (5 rows and 10 columns), resulting in a total of 50 squares.

• Step 2: Count the Shaded Squares.
  The top row, which is fully shaded, consists of 8 shaded squares.

• Step 3: Calculate the Fraction of the Shaded Area.
  The fraction that represents the shaded area is $\frac{\text{number of shaded squares}}{\text{total number of squares}} = \frac{8}{100}$.

• Step 4: Convert Fraction to Decimal.
  The fractional representation $\frac{8}{100}$ can also be expressed as a decimal, $0.08$.

Therefore, the shaded area represents $\frac{8}{100}$ or $0.08$ of the whole grid.

The large square grid is divided into smaller squares. Let's determine how many small squares there are in total.

• Step 1: Count the number of small squares along one side. From the SVG image, each side seems to have 10 smaller squares (since each section appears uniform and there are grids within both, rows, and columns).

• Step 2: Calculate the total number of smaller squares in the grid. Since it's a square, the total is $10 \times 10 = 100$ small squares.

• Step 3: Calculate what fraction of the whole one shaded square (the blue one) represents. The shaded area is one of these squares, so it represents $\frac{1}{100}$ of the entire grid.

Therefore, the shaded area represents $0.01$ or $\frac{1}{100}$ of the whole grid.

To solve this problem, we need to determine the fraction of the whole grid that is represented by the shaded (blue) area. The grid is a 10x10 layout, therefore containing a total of $10 \times 10 = 100$ equal-sized squares.

Step 1: We count the number of shaded squares in the grid. According to the illustration, there are 86 shaded squares.

Step 2: Calculate the fraction of the shaded area compared to the whole grid: $\frac{\text{Number of shaded squares}}{\text{Total number of squares}} = \frac{86}{100}$.

Step 3: Convert this fraction into a decimal. Dividing the numerator by the denominator gives us $0.86$.

Therefore, the shaded area represents $\frac{86}{100}$ of the total grid, which is equivalent to $0.86$.

This matches with the correct answer choice, which is: $0.86$ or $\frac{86}{100}$.

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

We'll write the fraction in the following way:

$\frac{033}{100}$

We'll then proceed to remove the unnecessary zeros as follows:

$\frac{33}{100}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

We will write the fraction as follows:

$\frac{065}{100}$

Finally We'll remove the unnecessary zeros as follows:

$\frac{65}{100}$

Note where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

Let's write the fraction in the following way:

$\frac{091}{100}$

Finally let's remove the unnecessary zeros as follows:

$\frac{91}{100}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

Let's write the fraction in the following way:

$\frac{001}{100}$

We'll then remove the unnecessary zeros as follows:

$\frac{1}{100}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

We will write the fraction in the following way:

$\frac{002}{100}$

We will then remove the unnecessary zeros as follows:

$\frac{2}{100}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

Let's write the fraction in the following way:

$\frac{004}{100}$

We'll then remove the unnecessary zeros as follows:

$\frac{4}{100}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

We'll write the fraction like this:

$\frac{006}{100}$

We'll then remove the unnecessary zeros as follows:

$\frac{6}{100}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

We will write the fraction in the following way:

$\frac{006}{100}$

We will then proceed to remove the unnecessary zeros and obtain the following:

$\frac{6}{100}$

Let's pay attention to where the decimal point is located in the number.

Remember:

One number after the zero represents tens

Two numbers after the zero represent hundreds

Three numbers after the zero represent thousands

And so on

In this case, there are two numbers after the zero, so the number is divided by 100

Let's write the fraction in the following way:

$\frac{009}{100}$

We'll then remove the unnecessary zeros as follows:

$\frac{9}{100}$