Decimal Fractions' Meaning: Graphical representation

The task is to determine which of the given figures correctly represents the decimal fraction 0.1.

To interpret 0.1, we recognize it as $\frac{1}{10}$. This indicates that in a graphical representation of 10 equal parts, 1 part should be shaded. Each figure is assumed to be divided into such equal parts.

Let's analyze the options:

• Choice 1: Shows 10 equal divisions with 1 part shaded. This potentially represents 0.1 since it shades exactly 1 of 10 parts.
• Choice 2: Shows 10 equal divisions with more than 1 part shaded. Thus, it represents more than 0.1.
• Choice 3: Shows 10 equal divisions with numerous parts shaded. It represents a number greater than 0.1.
• Choice 4: Shows a full shading, representing 1 (i.e., shading all 10 parts), clearly not 0.1.

Hence, the correct choice that correspond to 0.1 is Choice 1. This figure accurately shades exactly 1 out of 10 equal segments.

Therefore, the solution to the problem indicates that choice 1 correctly represents the decimal fraction 0.1.

To solve this problem, we'll identify the graphical representation of the decimal number $0.9$.

• Step 1: Understand that $0.9$ represents nine-tenths, so $9$ out of $10$ segments should be shaded.
• Step 2: Review the given figures to find which one has nine-tenths of its total area shaded.
• Step 3: Check that this representation corresponds directly to the given decimal value $0.9$.

Now, let's analyze the available choices:
Choice 1 represents the entire area shaded, which corresponds to $1.0$, not $0.9$.
Choice 2 has approximately three-tenths shaded, representing $0.3$, not $0.9$.
Choice 3 shows five-tenths shaded, which is $0.5$, not $0.9$.
Choice 4 displays nine out of ten sections shaded, accurately representing $0.9$.

Therefore, the correct figure is choice 4, which correctly represents the decimal fraction $0.9$.

The solution to the problem is choice 4.

To solve the problem of identifying which figure represents seven tenths, follow these steps:

• Step 1: Understand that the problem requires identification of a geometric representation for the fraction $\frac{7}{10}$ or decimal 0.7.
• Step 2: Each figure is divided into ten equal segments, representing one tenth each.
• Step 3: Carefully count the number of segments filled or shaded in each figure.

Now, let's apply these steps:

Step 1: We note that each figure is evenly divided into ten parts.

Step 2: By inspecting each option, you can see which has exactly seven segments shaded. This corresponds directly to seven out of ten segments, or seven tenths.

Step 3: Upon review, the figure corresponding to choice 3 shows exactly seven shaded segments out of ten.

Therefore, the solution to the problem is eminently found as choice 3, representing seven tenths.

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 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 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, 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 determine the place value of decimal $0.3$, we need to understand the structure of decimal numbers. In a decimal number system, each digit to the right of the decimal point represents a fractional part of a power of ten.

• Step 1: Identify the position of the digit '3'. In $0.3$, the digit '3' is in the first position to the right of the decimal point.
• Step 2: Determine the corresponding fractional place value. The first position to the right of the decimal point represents the tenths. Therefore, the place value of '3' in this position is three tenths.
• Step 3: Understand the implication. Since there are no other digits involved in this problem, the place value is simply three tenths, written as $\frac{3}{10}$.

However, none of the options provided are directly 'three tenths'. Upon reviewing the options' wording, we identify that 'thirty hundredths' can equivalently be expressed as $\frac{30}{100} = \frac{3}{10}$. Therefore, for the specific question and provided options, the place value of 0.3 is correctly identified as "Thirty hundredths".

Therefore, the solution to the problem is "Thirty hundredths".