Decimal Fractions - Advanced - Examples, Exercises and Solutions

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'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:

• 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, 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, 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, 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:

• 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 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 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, 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 $0.5$.

First let's fill in the zeros in the empty spaces as follows:

$21.52\\+03.40\\$Note that the decimal points are written one below the other.

Therefore, the positions of the decimal points correspond and thus the exercise is written in the correct form.

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

Note that the decimal points are not written one below the other. They do not correspond.

Therefore, the exercise is not written correctly.

To determine if the addition problem is set up correctly, we need to analyze how the numbers are aligned.

The given numbers for addition are $312.54$ and $1203.22$. When aligning these numbers for addition:

$\begin{array}{r} 312.54 \\ +1203.22 \\ \hline \end{array}$

We examine how the decimal points are positioned. For a correct setup, the decimal points should be aligned vertically. However, in the visual provided:

• The decimal point in $312.54$ is positioned one place to the right compared to the decimal in $1203.22$.

• The alignment should have appeared as $\begin{aligned} &\phantom{00}312.54 \\ &+1203.22 \end{aligned}$ to be correct, but it does not.

Since the decimal points are not vertically aligned, the addition is set up incorrectly.

Therefore, the statement regarding the positioning of the decimal points is Not true.

First let's fill the zeros in the empty space as follows:

$006.310\\+216.222\\\$

Here We should note that the decimal points are written one below the other.

Therefore, the exercise is written in the appropriate form.