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

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 $3$.

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 $2.6$.

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 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 multiplying the decimal number $2.78$ by $10$, we'll apply the rule of moving the decimal point:

• Step 1: Identify the decimal number, which is $2.78$.
• Step 2: Recognize that when multiplying by $10$, the decimal point shifts one place to the right.

By shifting the decimal point one position right, $2.78$ becomes $27.8$.

This operation shows that multiplying by $10$ effectively scales the value up by one power of ten.

Therefore, the solution to the problem is $27.8$.

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, 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.

To solve this problem, here's a step-by-step approach:

• First, identify the decimal number: $3.41$.
• Understand that multiplying by $10$ involves moving the decimal point one place to the right.
• Shift the decimal point in $3.41$ from between $3$ and $4$ to between $4$ and $1$, resulting in the number $34.1$.

Thus, the solution to the problem is $34.1$.

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: $26.6$.

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

• Step 1: Identify the given decimal number: $0.7$.
• Step 2: Recognize that multiplying by $10$ shifts the decimal point one place to the right.
• Step 3: Move the decimal point one place to the right from $0.7$ to $7.0$, which can be expressed simply as $7$.

Now, let's work through each step:

Step 1: We are given the number $0.7$ to multiply by $10$.
Step 2: Multiplying by $10$ moves the decimal point one position to the right.
Step 3: Performing this shift, $0.7$ becomes $7.0$, which simplifies to $7$.

Therefore, the solution to the problem is $7$.

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 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 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: Identify the given number and confirm it is 7.81.
• Step 2: Understand that to multiply by 10, we move the decimal point one place to the right.
• Step 3: Perform the operation and identify the resulting number.

Now, let's work through each step:

Step 1: We start with the decimal number $7.81$.

Step 2: To multiply by 10, move the decimal point one position to the right:

$7.81$ becomes $78.1$ when multiplied by 10.

Step 3: Thus, the final result of multiplying $7.81 \times 10$ is $78.1$.

Therefore, the solution to the problem is $78.1$.

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 $1.131$.