Decimal Fractions' Meaning - Examples, Exercises and Solutions

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

• Step 1: Understand the problem of finding the number of tenths in 1.3.
• Step 2: Note that the decimal number 1.3 is composed of the whole number 1 and the decimal fraction 0.3.
• Step 3: Recognize that the tenths place is the first digit after the decimal point.

Now, let's work through each step:

Step 1: The problem asks us to count the number of tenths in the decimal number 1.3. This involves understanding the place value of each digit.

Step 2: In the decimal 1.3, the digit '1' represents the whole number and does not contribute to the count of tenths. The digit '3' is in the tenths place.

Step 3: Since the digit '3' is in the tenths place, it denotes 3 tenths or the fraction $\frac{3}{10}$.

Therefore, the number of tenths in 1.3 is $3$.

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

• Examine the given number 0.4.
• Identify and list all digits represented in this decimal.
• Count the occurrences of the digit '1'.

Now, let's work through each step:
Step 1: The number given is 0.4. This number is composed of the digits '0', '.', and '4'.
Step 2: Identify any '1's among these digits. There are no '1's in this sequence of digits.
Step 3: Thus, the count of the digit '1' in the number 0.4 is zero.

Therefore, the number of ones in the number 0.4 is $0$.

To solve this problem, we'll examine the given decimal number, $0.07$, to identify how many '1's it contains.

Let's break down the number $0.07$:

• The digit to the left of the decimal is $0$, which is the ones place. It is not '1'.
• The first digit after the decimal point is $0$, which represents tenths. This is also not '1'.
• The next digit is $7$, which represents hundredths. This digit is also not '1'.

None of the digits in the number $0.07$ are equal to '1'.

Therefore, the number of ones in $0.07$ is 0.

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

• Step 1: Define the place value of each digit in the decimal number.
• Step 2: Identify the specific digit in the hundredths place.
• Step 3: Determine the number of hundredths in 0.96.

Now, let's work through each step:

Step 1: Consider the decimal number $0.96$. In decimal representation, the digit immediately after the decimal point represents tenths, and the digit following that represents hundredths.

Step 2: In the number $0.96$, the digit $9$ is in the tenths place, and the digit $6$ is in the hundredths place.

Step 3: Therefore, the number of hundredths in $0.96$ is $6$.

Thus, the solution to the problem is that there are 6 hundredths in the number $0.96$.

To solve this problem, we need to examine the decimal number $0.81$ and count the number of '1's present:

• The first digit after the decimal point is $8$.
• The second digit after the decimal point is $1$.

Now, count the number of '1's in $0.81$:

There is only one '1' in the entire number $0.81$ because it appears only once after the decimal point.

Thus, the total number of ones in $0.81$ is 0, since the task is to count ones in the whole number, and there are no ones in the integer part of $0$, nor in the remaining digits $8$.

Therefore, the solution to the problem is $0$, which corresponds to choice 3.

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.

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 solve this problem, we need to apply the place value system to construct the number correctly:

• Step 1: Calculate the contribution of the hundreds place.
  Given: 4 hundreds, which contributes $4 \times 100 = 400$.
• Step 2: Calculate the contribution of the tens place.
  Given: 6 tens, which contributes $6 \times 10 = 60$.
• Step 3: Calculate the contribution of the ones place.
  Given: 5 ones, which contributes $5 \times 1 = 5$.
• Step 4: Sum up all the contributions to find the required number:
  $400 + 60 + 5 = 465$

Therefore, the number formed according to the given place values is $465$.

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

• Step 1: Assign each number to the correct place value.
• Step 2: Construct the number by adding each weighted position.

Now, let's work through each step:
Step 1: We have three digits to place:
- We assign **9** to the ones (units) position.
- We assign **3** to the tens position.
- We assign **1** to the hundreds position.

Step 2: Combine these placements:
- The number is constructed as follows: $100 \times 1 + 10 \times 3 + 1 \times 9$
- This simplifies to: $100 + 30 + 9 = 139$.

Upon comparing with the provided answer choices, the correct choice is clearly $\boxed{139}$.

Therefore, the solution to the problem is $139$.