Decimal Fractions Practice Problems - Advanced Math

To solve this problem, let's analyze the shaded area in terms of grid squares:

• Step 1: The top rectangle in the grid is completely filled. Let's count the shaded squares horizontally: There are 10 squares across aligned vertically in 1 row, giving $1$ as the shaded area.
• Step 2: The bottom rectangle is partially filled. Observe it spans $6$ squares horizontally by $1$ square height in the grid row. The shaded area will, therefore, be $0.6$ as it spans only $60\%$ of the horizontal extent.
• Step 3: Add both shaded areas of the rectangles from step 1 and step 2: $1$ (top) and $0.6$ (bottom).

Thus, the total shaded area is $1 + 0.6 = 1.6$.

Therefore, the solution to the problem is $1.6$.

To solve this problem, we'll follow a few simple steps to calculate the shaded area by counting strips and converting to a decimal:

• Step 1: Identify the total number of vertical strips in the entire rectangle. From the diagram, there are 10 strips in total.
• Step 2: Count the number of shaded vertical strips. According to the diagram, 5 strips are shaded.
• Step 3: Write the fraction of the shaded area relative to the total area. The fraction is $\frac{5}{10}$.
• Step 4: Simplify the fraction, which is already simplified, and then convert it to a decimal. $\frac{5}{10} = 0.5$.

Therefore, the solution to the problem is $0.5$.

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

• Step 1: Identify the total number of divisions in the grid.
• Step 2: Count the number of shaded divisions.
• Step 3: Calculate the fraction of the shaded area relative to the total.

Now, let's work through each step:
Step 1: The grid is divided into 10 equal vertical columns.
Step 2: Of these columns, 1 column is shaded.
Step 3: Since there are 10 columns in total, the shaded area represents $\frac{1}{10}$ of the total area.

Finally, the fraction $\frac{1}{10}$ can be expressed as the decimal $0.1$.

Therefore, the numerical value of the shaded area is $0.1$.

To solve this problem, let's follow the outlined plan:

• Step 1: Count the number of shaded sections.
• Step 2: Count the total number of sections in the rectangle.
• Step 3: Express the number of shaded sections as a fraction of the total sections.
• Step 4: Convert this fraction to a decimal to find the numerical value.

Now, let's apply these steps:
Step 1: The given diagram shows that there are 4 vertical stripes shaded.
Step 2: The total number of vertical stripes (including both shaded and unshaded) is 10.
Step 3: The fraction of shaded area is $\frac{4}{10}$.
Step 4: Convert $\frac{4}{10}$ to a decimal. This equals $0.4$.

Therefore, the numerical value of the shaded area is 0.4.

To reduce the decimal fraction $0.99000$, trailing zeros are removed. Therefore, $0.99000$ simplifies to $0.99$. Hence, the reduced fraction is $0.99$.