Decimal Fractions' Meaning - Examples, Exercises and Solutions

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, 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, let's carefully examine the decimal number $0.73$ digit by digit:

• The first digit after the decimal point is $7$.
• The second digit after the decimal point is $3$.

We observe that there are no digits in the sequence of $0.73$ that are the number '1'. Therefore, there are no '1's in the decimal number $0.73$.

Thus, the number of ones in the number $0.73$ is 0.

The correct choice, given the options, is choice id 1: 0.

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.