Converting a Decimal Fraction to a Mixed Number

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:

$\frac{038}{100}$

We'll then remove the unnecessary zeros as follows:

$\frac{38}{100}$

To solve this problem, we'll follow these steps:

• Step 1: Count the total number of equal sections in the diagram.
• Step 2: Determine how many sections are shaded in blue.
• Step 3: Use the fraction formula $\frac{\text{shaded sections}}{\text{total sections}}$ to find the portion represented by the shaded area.
• Step 4: Convert the fraction to a decimal.

Now, let's work through each step:

Step 1: Upon examining the diagram, we observe that the grid is divided into 10 vertical sections. Each section is presumably equal in area.

Step 2: There is 1 shaded section, which is the first vertical column on the left.

Step 3: Using the fraction formula, the part of the whole represented by the shaded section is $\frac{1}{10}$, because there is 1 shaded section out of 10 total sections.

Step 4: We convert the fraction $\frac{1}{10}$ into its decimal form, which is $0.1$.

Therefore, the solution to the problem is the shaded area represents $0.1$ or $\frac{1}{10}$ of the whole.

This corresponds to choice 3: $0.1$ and $\frac{1}{10}$.

To solve this problem, we will follow these steps:

• Step 1: Count the total number of equal vertical sections in the grid.
• Step 2: Count the number of shaded (blue) sections.
• Step 3: Determine the fraction of the whole that is shaded.
• Step 4: Simplify the fraction, if needed, and express it as a decimal.

Now, let's execute these steps:

Step 1: By examining the diagram, we observe there are 10 equal vertical sections in total.

Step 2: Of these sections, 2 are shaded blue.

Step 3: The fraction of the shaded area compared to the whole is $\frac{2}{10}$.

Step 4: Simplify $\frac{2}{10}$ to $\frac{1}{5}$, but since we are asked to express it as part of 10 parts, $\frac{2}{10}$ remains an accurate choice. The decimal equivalent is $0.2$.

Therefore, the shaded part of the whole is $\frac{2}{10}$ or $0.2$.

Among the given choices, the correct answer is: $\frac{2}{10}$ or $0.2$.

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 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 $\frac{8}{10}$.