Decimal Fractions' Meaning: Visual representation of a fraction

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 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, 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.