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

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 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 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 this problem, we'll follow these steps:

• Step 1: Identify the given number, which is $65.2$.
• Step 2: Apply the rule for dividing a decimal by 10: Shift the decimal point one place to the left.
• Step 3: Verify the result by ensuring the computation is accurate.

Now, let's work through each step:
Step 1: The problem gives us the number $65.2$.
Step 2: We'll divide by 10 by shifting the decimal point one place left. This changes $65.2$ to $6.52$.
Step 3: Checking our work, $6.52$ is indeed the correct result of shifting the decimal point left.

Therefore, the solution to the problem is $6.52$.

To solve this problem, we need to divide $581.8$ by $10$.

• Step 1: Identify the decimal point in the number $581.8$, which is between the $1$ and $8$.
• Step 2: Move the decimal point one place to the left as per the rule of dividing by 10. This step transforms $581.8$ into $58.18$.
• Step 3: Write down the resulting number.

Therefore, when we divide $581.8$ by $10$, the result is $58.18$.

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'll follow these steps:

• Step 1: Identify the current position of the decimal point in the number $51.4$.
• Step 2: Use the rule for dividing by $10$, which involves moving the decimal point one place to the left.
• Step 3: Obtain the resultant number after moving the decimal point.

Now, let's work through each step:

Step 1: The number given is $51.4$, and the decimal point is after the $1$.

Step 2: According to the division rule for decimals, when dividing by $10$, we move the decimal point one place to the left, making it $5.14$.

Step 3: The resulting number after the decimal point is moved is therefore $5.14$.

Thus, the solution to the problem is $5.14$.

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 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 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 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 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 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 $7$.

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, 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 $34.1$.