Multiplying and Dividing Decimal Fractions by 10, 100, etc. - Examples, Exercises and Solutions

To solve the problem $0.07 \times 10$, we recognize that multiplying a decimal number by 10 involves shifting the decimal point one place to the right.

Let's work through the steps:

• Initially, the decimal number $0.07$ has a decimal point located between the "0" in the tenths place and "07".
• When multiplying by 10, we shift the decimal point one place to the right. This changes the number from $0.07$ to $0.7$.

The decimal point's new position results in the number $0.7$, representing the product of the original number and 10.

The solution to the problem is $0.7$.

To solve this problem, we'll follow this straightforward approach:

• Since we are multiplying by $10$, we need to shift the decimal point in the number $1.004$ one place to the right.

Now, let's perform the calculation:

The number $1.004$ has a decimal point after the first digit, and when we shift the decimal one place to the right, it moves between $0$ and $0$, resulting in $10.04$.

Therefore, the product of $1.004$ multiplied by $10$ is $10.04$.

Thus, the solution to the problem is $10.04$.

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

• Step 1: Identify the given information: $111.1$ needs to be divided by $10$.
• Step 2: Apply the rule for dividing decimals by 10: shift the decimal point in the number $111.1$ one place to the left.

Now, let's work through these steps in detail:

In Step 1, we confirm that the problem provides the number $111.1$ to be divided by $10$.

In Step 2, we apply the rule of decimal division by shifting the decimal point in $111.1$ one place to the left. This means the decimal moves from between the "111" and the "1" to between the "11" and "11". Thus, the number becomes $11.11$.

Therefore, the solution to the problem is $11.11$.

To solve this problem, we aim to multiply the decimal number 1.14 by 10. When multiplying a decimal number by 10, we shift the decimal point one place to the right. Let's follow these steps to solve the problem:

• Step 1: Identify the position of the decimal point in the number 1.14. It is currently between the digits 1 and 4.
• Step 2: Shift this decimal point one position to the right as we are multiplying by 10. After shifting, the decimal point will be placed to the right of the digit 4.

Therefore, moving the decimal point one position to the right transforms 1.14 into 11.4.

Hence, the product of $1.14 \times 10$ is $11.4$.

To solve this problem, follow these steps:

• Step 1: Identify the decimal number given in the problem. In this case, it is 11.31.
• Step 2: Note that we are instructed to divide this number by 10.
• Step 3: When dividing a number by 10, simply move the decimal point in the original number one place to the left.

Now, let's perform the calculation:

In the number 11.31, the decimal point is after the first "1". To divide by 10, move the decimal point one place to the left, resulting in the number:

$1.131$

This is the correct result of dividing 11.31 by 10.

Therefore, the solution to the problem is $1.131$.

To solve this division problem, we will follow these steps:

• Step 1: Identify the initial position of the decimal point in the number $12.2$.
• Step 2: Apply the rule for division by $10$, which involves moving the decimal point one place to the left.
• Step 3: Confirm the resulting value after the decimal shift.

Now, let's proceed with addressing each step:

Step 1: The number $12.2$ has its decimal point positioned after the digit $2$.

Step 2: Dividing by $10$ means moving this decimal point one place to the left, resulting in the decimal point being placed after the number $1$, turning $12.2$ into $1.22$.

Step 3: Thus, the value obtained is $1.22$.

Therefore, the solution to the problem is $1.22$.

To solve the problem, we'll use a straightforward approach:

• Step 1: Recognize that dividing by 10 moves the decimal point one place to the left.
• Step 2: Start with 13.61.
• Step 3: Move the decimal point one place left results in 1.361.

Now, let's apply these steps to calculate:

Starting with $13.61$, when dividing by 10, the decimal moves one position to the left:

$13.61 \rightarrow 1.361$.

Thus, the solution to the division is $1.361$.

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

• Step 1: Identify the position of the decimal point in the number 1.4, which is between the 1 and the 4.
• Step 2: Multiply by 10 by moving the decimal point one place to the right.

Now, let's work through each step:

Step 1: The decimal point in 1.4 is currently right after the 1.
Step 2: When multiplying by 10, move the decimal point one place to the right. This transforms 1.4 into 14.0, which simplifies to 14.

Therefore, the solution to the problem is $14$.

To solve the problem of multiplying 1.52 by 10, we follow these simple steps:

• Step 1: Understand that multiplying a decimal number by 10 involves shifting the decimal point one place to the right.
• Step 2: Start with the number 1.52.
• Step 3: Shift the decimal point one place to the right to get 15.2.

Let's perform these steps:
Starting with 1.52, when we shift the decimal point one place to the right, we move from 1.52 to 15.2. This is because multiplying by 10 increases the value by one order of magnitude.

Thus, the product of $1.52 \times 10$ is $15.2$. Therefore, the correct answer choice is $15.2$.

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

• Step 1: Understand the operation needed: multiply the decimal 0.3 by 10.
• Step 2: Apply the rule for multiplying by powers of 10.
• Step 3: Execute the operation and write down the result.

Now, let's work through each step:
Step 1: We need to multiply 0.3 by 10. Multiplying by 10 involves shifting the decimal point.
Step 2: Using the rule for multiplying decimals by 10, we shift the decimal point in 0.3 one place to the right.
Step 3: Originally, the decimal point in 0.3 is after the '3'. After shifting it right by one place, we get '3.0'. This is equivalent to $3$.

Therefore, the solution to the problem is $3$.

To solve this problem, we'll use the property that states: when we multiply a decimal number by $10$, we move its decimal point one place to the right.

Let's work through the steps:

• Step 1: Identify the number and its decimal place. The number $2.7$ has a decimal point between $2$ and $7$.
• Step 2: Since we are multiplying by $10$, move the decimal point one place to the right. Moving the decimal point means $2.7$ becomes $27.$.
• Step 3: Write down the resulting number. After moving the decimal point, the number is $27$.

Therefore, the product of $2.7 \times 10$ is $27$.

To solve $20.1 \div 10$, we follow these steps:

• Step 1: Identify that we are dividing by 10, so we will move the decimal point one place to the left.
• Step 2: Start with the number 20.1 and move the decimal point one place left to get 2.01.
• Step 3: Write the new number after shifting the decimal, which gives us 2.01.

After carrying out these steps, we find that the solution to the problem is $2.01$.

To solve this problem, let's multiply the decimal number $2.31$ by $10$:

• Step 1: Understanding the multiplication by 10.
  When a decimal number is multiplied by 10, we shift the decimal point one place to the right.

• Step 2: Apply the rule to $2.31$.
  The decimal point in $2.31$ is between 2 and 3. Move it one position to the right:

• Step 3: After the shift, the decimal point will be positioned after the 3, resulting in $23.1$.

Therefore, the solution to the problem $2.31 \times 10$ is $23.1$.

Among the choices given, $23.1$ corresponds to choice 1.

We will solve the problem by multiplying $0.26$ by $10$. When multiplying a decimal by $10$, the decimal point moves one place to the right.

Let's follow the steps:

• Recognize our initial number: $0.26$.
• To multiply by $10$, shift the decimal point one position to the right. This changes $0.26$ to $2.6$.

Therefore, multiplying $0.26$ by $10$ gives us the result $2.6$.

The solution to the problem is $2.6$.

We need to multiply the number $2.66$ by $10$. To do this, follow these steps:

• Step 1: Identify the initial decimal number: $2.66$.
• Step 2: Understand that multiplying by $10$ involves moving the decimal point one place to the right.
• Step 3: Shift the decimal point of $2.66$ from its original position between $2$ and $6$ to between $6$ and $6$, which gives us $26.6$.

Therefore, after multiplying $2.66$ by $10$, the result is $26.6$.

The correct answer, based on the available choices, is: $26.6$.