Decimal Fractions - Advanced - 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.

Since there are two digits after the decimal point, we divide 36 by 100:

$\frac{36}{100}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 4, so:

$\frac{36:4}{100:4}=\frac{9}{25}$

Since there is one digit after the decimal point, we divide 5 by 10:

$\frac{5}{10}$

Now let's find the highest number that divides both the numerator and the denominator.

In this case, the number is 5, so:

$\frac{5:5}{10:5}=\frac{1}{2}$

Since there are three digits after the decimal point, we divide 350 by 1000:

$\frac{350}{1000}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 50, so:

$\frac{350:50}{1000:50}=\frac{7}{20}$

Since there are three digits after the decimal point, we divide 630 by 1000:

$\frac{630}{1000}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 10, so:

$\frac{630:10}{1000:10}=\frac{63}{100}$

To solve this problem, we will add the decimal numbers 0.75 and 0.35 by aligning them according to their decimal points:

• Step 1: Align the numbers vertically by their decimal points:

  $\begin{array}{c} \phantom{0}\\ \phantom{0} \quad 0.75 \\ + \quad 0.35 \\ \hline \end{array}$

• Step 2: Add the digits starting from the rightmost column (hundredths place):

  - Hundredths place: $5 + 5 = 10$. Write 0 and carry over 1 to the tenths place.
  - Tenths place: $7 + 3 + 1 = 11$. Write 1 and carry over 1 to the units place.
  - Units place: $0 + 0 + 1 = 1$.

• Step 3: Write the final sum by placing the decimal point correctly below the decimal points of the addends:

  $\begin{array}{c} 0.75\\ + 0.35\\ \hline 1.10\\ \end{array}$

The sum of 0.75 and 0.35 is therefore $\textbf{1.10}$, which can be simplified to $\textbf{1.1}$ by removing the trailing zero after the decimal point.

The correct answer is, therefore, $\textbf{1.1}$, corresponding 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.

To solve the division problem $2.6 \div 0.1$, we can simplify the division by eliminating the decimal in the divisor:

• Multiply both the dividend $2.6$ and the divisor $0.1$ by 10 to get rid of the decimal in the divisor. This gives $2.6 \times 10 = 26$ and $0.1 \times 10 = 1$.
• Now, the division simplifies to $26 \div 1$.
• Dividing $26$ by $1$ gives us $26$.

Thus, the solution to the division problem $2.6 \div 0.1$ is $26$.

Since there is one digit after the decimal point, we divide 8 by 10:

$\frac{8}{10}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 2, so:

$\frac{8:2}{10:2}=\frac{4}{5}$

Since there are two digits after the decimal point, we divide 58 by 100:

$\frac{58}{100}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 2, so:

$\frac{58:2}{100:2}=\frac{29}{50}$

Since there are two digits after the decimal point, we divide 75 by 100:

$\frac{75}{100}$

Now let's find the highest number that divides both the numerator and denominator.

In this case, the number is 25, so:

$\frac{75:25}{100:25}=\frac{3}{4}$