Multiplying and Dividing Decimal Fractions by 10, 100, etc.: Division by 10

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 need to divide $0.3$ by $10$. We can achieve this by using the following steps:

• Step 1: Understand that dividing by $10$ means moving the decimal point one place to the left.
• Step 2: Currently, the number is $0.3$. To divide by $10$, shift the decimal one place left to obtain the new value.
• Step 3: After moving the decimal point, the new value becomes $0.03$.

This simple operation demonstrates that when dividing by powers of ten, the decimal point moves to the left by as many places as there are zeros in the power (one zero here, for dividing by ten).

Therefore, the solution to the problem is $\text{0}.03$.

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

• Step 1: Understand decimal division by powers of ten.
• Step 2: Perform the decimal point shift.
• Step 3: Compare the result with the provided options.

Now, let's work through each step:

Step 1: The operation involves division by $10$, which is equivalent to shifting the decimal point of the number one place to the left. We begin with the number $1.71$.

Step 2: In $1.71$, the decimal point is moved one place to the left, changing it to $0.171$.

Step 3: Check this answer against the options given:

• Option 1: $0.17$
• Option 2: $0.71$
• Option 3: $0.171$
• Option 4: $0.711$

The correct answer is Option 3: $0.171$.

Therefore, the solution to the problem is $0.171$.

To solve this problem, let's follow these steps:

• Step 1: Identify the given number and divisor.
• Step 2: Understand how dividing by 10 affects decimal placement.
• Step 3: Perform the division and verify the result with the choices provided.

Now, let's work through each step:

Step 1: The problem gives us the number $2.2$ and requires dividing it by $10$.

Step 2: When dividing a number by $10$, you move the decimal point one place to the left. This is a result of how the base-10 system works; dividing by a power of 10 shifts the decimal point left.

Step 3: In the number $2.2$, the decimal is currently after the numeral "2." Moving the decimal one place left, we have:

$2.2 \rightarrow 0.22$

Therefore, the result of $2.2 \div 10$ is $\textbf{0.22}$.

To ensure accuracy, we compare this result with the provided choices. Choice number 3, $0.22$, matches our solution.

Thus, the solution to the problem is $0.22$.

To solve this problem, follow these steps:

• Step 1: Recognize that we are dividing $0.1$ by $10$.
• Step 2: Apply the rule for dividing by $10$, which involves shifting the decimal point in $0.1$ one place to the left.

Let's solve the problem:

Step 1: We have the number $0.1$, and we need to divide it by $10$.
Step 2: Since dividing by $10$ shifts the decimal point one place to the left, move the decimal in $0.1$ one place left.
Therefore, $0.1$ becomes $0.01$ after shifting the decimal point.

Thus, the solution to the problem is $\boxed{0.01}$.

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

• Step 1: Understand that dividing by 10 shifts the decimal point one place to the left.
• Step 2: Apply this knowledge to the number 0.8.

Now, let's work through each step:

Step 1: The number given is $0.8$. We need to divide this number by 10. When dividing by 10, we shift the decimal point one place to the left.

Step 2: Shifting the decimal point of $0.8$ one place to the left results in $0.08$.

Therefore, the solution to the problem is $0.08$.

To solve the problem of dividing 1.65 by 10, we apply the rule for decimal division by powers of ten:

• Step 1: Identify the given number, which is 1.65.
• Step 2: Apply the rule for division by 10. This involves moving the decimal point one place to the left.
• Step 3: Starting with 1.65, move the decimal point one place to the left to get 0.165.

Therefore, after dividing 1.65 by 10, we obtain $0.165$.

To solve the problem, we will use the rule for dividing a decimal by $10$, which requires moving the decimal point one position to the left:

• Identify the current decimal position in the number $0.061$, which is between the zero and six in $0.061$.

• Move the decimal point one position to the left to divide by $10$.

• After moving, the decimal point between $0$ and $6$ is positioned before the first $0$, resulting in $0.0061$.

Thus, the result of dividing $0.061$ by $10$ is $\mathbf{0.0061}$.

The correct choice among the given options is Choice 2 with the value $0.0061$

To solve this problem, we need to perform division of the decimal number $113.4$ by $10$.

• Step 1: Understand the operation: Division by $10$ involves moving the decimal point one position to the left.
• Step 2: Locate the decimal point in the number $113.4$. It is between the digits $3$ and $4$.
• Step 3: Move the decimal point one position to the left to divide by $10$.

By moving the decimal one position to the left, the number $113.4$ becomes $11.34$.

Therefore, the result of dividing $113.4$ by $10$ is $\mathbf{11.34}$.

To solve this problem, let's follow a simple approach using the decimal shifting rule:

• Step 1: Identify the initial decimal point position in 23.1, which is between '3' and '1'.
• Step 2: To divide by 10, move the decimal point one position to the left.

Now, moving the decimal point one place to the left converts 23.1 to 2.31.

Therefore, the solution to the problem is $2.31$, which corresponds to choice .

To solve this problem, we need to divide the number 4.61 by 10.

When dividing a decimal by 10, we move the decimal point one place to the left. This is a standard rule of arithmetic for dealing with powers of ten:

• Starting decimal: $4.61$
• Move the decimal point one place left: $0.461$

Therefore, the result of dividing 4.61 by 10 is $\boxed{0.461}$.

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

• Step 1: Identify the given decimal number, $0.123$.
• Step 2: Apply the rule for dividing a decimal by $10$, which involves moving the decimal point one place to the left.
• Step 3: Perform the movement of the decimal point.

Now, let's work through each step:

Step 1: We have the decimal number $0.123$.

Step 2: The rule for dividing by $10$ tells us to move the decimal point one place to the left.

Step 3: Moving the decimal point one place to the left, $0.123$ becomes $0.0123$.

Therefore, the solution to the problem is $0.0123$.

Checking the answer against the choices, the correct choice is: : $0.0123$.

To solve this problem of dividing 2.6 by 10, we will observe the following steps:

• Step 1: Recognize that dividing by 10 shifts the decimal point one place to the left.
• Step 2: Identify the position of the decimal point in the number 2.6, which is immediately after the 2.
• Step 3: Move the decimal point one place to the left, changing 2.6 to 0.26.

Thus, when you divide 2.6 by 10, the result is $0.26$.

The correct answer is confirmed to be :

$0.26$