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

To solve this problem, we will follow these steps:

• Step 1: Start with the decimal number 0.08.
• Step 2: Recognize that multiplying by 100 is equivalent to moving the decimal point two places to the right.
• Step 3: Move the decimal point in 0.08:
  • Original: 0.08 (decimal between 0 and 8)
  • Move one place: becomes 0.8
  • Move another place: becomes 8.0
  • Simplify 8.0 to 8

Therefore, multiplying $0.08$ by $100$ gives us $8$.

Conclusion: The solution to the problem is $8$. The correct choice from the options given is choice 3.

To solve this problem, we'll focus on the rule for multiplying decimal fractions by powers of 10:

• Move the decimal point to the right for each power of ten involved in the multiplication.

• For $100$, we move the decimal point two places to the right.

Let's apply this to our problem:

The given number is $0.314$.

Step 1: Identify the number of decimal places in $0.314$, which is 3 digits long: "314".

Step 2: Multiplying $0.314$ by $100$ requires us to move the decimal point two places to the right.

Before moving the decimal point:

$0.314$

Move the decimal point two places right:

$3.14$

Effectively, the number becomes $31.4$.

Hence, the result of $0.314 \times 100 = 31.4$.

Therefore, the solution to the problem is $31.4$.

The correct answer choice from the options is:

$31.4$

To solve the problem $0.72 \times 100$, we need to understand how multiplying by $100$ affects a decimal number.

Multiplying a number by $100$ means shifting its decimal point two places to the right. Here’s a step-by-step explanation:

• Step 1: The original number is $0.72$. Observe the decimal position just after the zero.
• Step 2: Move the decimal point two places to the right because $100$ has two zeros.
  - Moving it one place to the right gives $7.2$.
  - Moving it a second place gives $72$.
• Step 3: The number becomes $72$, which is now a whole number.

Thus, the product of $0.72 \times 100$ is $72$.

To solve this mathematical problem, let's carry out the following steps:

• Step 1: Identify the initial position of the decimal point in the number. The number is $1.004$, where the decimal point is after the first digit (1).
• Step 2: Multiply by 100. Multiplying a decimal by 100 shifts the decimal point two places to the right.
• Step 3: Move the decimal point in $1.004$ two places to the right, changing it from $1.004$ to $100.4$.

The decimal originally in the thousandths position now moves to the tenths position.

Therefore, the result of multiplying $1.004 \times 100$ is $\boxed{100.4}$.

Looking at the answer choices, we see that the correct answer corresponds to choice 3, which is $100.4$.

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

• Step 1: Identify the given number as $1.031$.
• Step 2: We'll apply the rule of moving the decimal point two places to the right, as we are multiplying by $100$.

Now, let's work through each step:
Step 1: The given number is $1.031$.
Step 2: Multiplying by $100$ involves moving the decimal two places to the right:
- Starting with $1.031$, the decimal goes from between '1' and '0' to between '3' and '1', resulting in $103.1$.

Therefore, the solution to the problem is $103.1$.

To solve this problem, we will perform a simple multiplication operation involving a decimal.

Firstly, consider the number $1.08$. When multiplying a decimal number by $100$, we can shift the decimal point two places to the right. This change reflects the fact that the number being multiplied is equivalent to increasing its value by a factor of $100$.

For $1.08$:
Original position: $1.08$ (decimal point after the second '1')
After shifting two places to the right, the number becomes $108.0$, which can be written simply as $108$ since the decimal point followed by zero does not change the value of the integer.

Therefore, the calculation yields the result: $1.08 \times 100 = 108$.

In conclusion, the solution to the problem is $108$.

To solve the problem of multiplying 1.09 by 100, follow these steps:

• Step 1: Recognize the multiplication of a decimal by 100 requires shifting the decimal point two places to the right.
• Step 2: Start with the number $1.09$.
• Step 3: Shift the decimal point two places to the right:
  From $1.09$ to $109.$ (The final decimal point is not necessary to write).

Therefore, the result of $1.09 \times 100$ is $109$.

The correct answer from the multiple choices given is option 2: $109$.

To solve the problem of finding $11.41 \times 100$, we'll follow these steps:

• Step 1: Understand the operation needed - multiplying by 100 involves moving the decimal point two places to the right.
• Step 2: Identify the initial position of the decimal point in the number 11.41. Initially, it is between 11 and 41.
• Step 3: Move the decimal two places to the right. This results in the number shifting from 11.41 to 1141.0.
• Step 4: Simplify by removing the unnecessary decimal zero, resulting in the final value of 1141.

Therefore, the solution to the problem $11.41 \times 100$ is $1141$.

To solve the problem of multiplying $1.313 \times 100$, we follow these steps:

• Step 1: Begin with the number $1.313$, observing where the decimal point is placed.
• Step 2: Multiplying by 100 requires moving the decimal point two places to the right. Initially, the decimal is after the first digit: $1.3\textbf{13}$.
• Step 3: Move the decimal point two places right: after the two shifts ($1.313 \rightarrow 13.13 \rightarrow 131.3$), we identify the new number.

This results in the number being $131.3$.

Thus, the correct answer is $131.3$.

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

• Step 1: Recognize that multiplying by 100 involves moving the decimal place two positions to the right.
• Step 2: Apply this technique to the number 1.62.
• Step 3: Confirm the final placement of the decimal and the resulting number.

Now, let's work through each step:
Step 1: We begin with the decimal number 1.62. Since we are multiplying by 100, we will move the decimal point two places to the right.
Step 2: Shifting the decimal two places right, we get 162.00. The zeros do not affect the value, so we can also write this as 162.
Step 3: Confirming, $1.62 \times 100 = 162$.

Therefore, the solution to the problem is $162$.

To solve the problem $2.001 \times 100$, we need to apply the fundamental property of multiplying a decimal number by a power of ten.

• Step 1: Identify that $100 = 10^2$. This means we must move the decimal point in $2.001$ two places to the right.
• Step 2: Take the number $2.001$ and move the decimal point two places right:
  - Start: $2.001$
- After moving the first place: $20.01$ (Decimal point now between 0 and 0)
- After moving the second place: $200.1$ (Decimal point now after the digit 1).

Thus, the product of $2.001 \times 100$ is $200.1$.

Therefore, the final answer is $200.1$, which corresponds to choice 2.

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

• Step 1: Identify the original position of the decimal point in 3.412.
• Step 2: Shift the decimal point two places to the right because we are multiplying by 100.
• Step 3: Write down the new number after shifting the decimal point.

Now, let's perform the solution:
Step 1: In the number 3.412, the decimal point is initially between the 3 and the 4.
Step 2: We shift this decimal point two places to the right, which changes the value to 341.2.
Step 3: The resulting number after this operation is 341.2.

Therefore, the solution to the problem is $341.2$.

To solve the problem of multiplying $4.16$ by $100$, we follow specific steps:

• Step 1: Identify the Original Position of the Decimal
  The number $4.16$ has a decimal point between the 4 and the 1, giving it two decimal places.
• Step 2: Apply the Multiplication Operation
  Multiplying by $100$ involves moving the decimal point two places to the right because $100$ has two zeros.
• Step 3: Shift the Decimal Point
  By shifting the decimal point two places to the right, $4.16$ becomes $416.$
• Step 4: Verify Against Answer Choices
  $416$ matches choice number 2 in the given multiple-choice list.

Therefore, the solution to the problem is $416$.

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

• Step 1: Identify the initial position of the decimal point in $12.21$, which is between the digits $2$ and $1$.
• Step 2: Shift the decimal point two places to the right. This movement changes $12.21$ to $1221$.
• Step 3: Confirm the resulting number, $1221$.

By multiplying $12.21$ by $100$, we shift the decimal point two spaces to the right, resulting in the number $1221$.

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

• Step 1: Understand the operation of multiplying a decimal by 100.
• Step 2: Apply the method of shifting the decimal point to the right.
• Step 3: Confirm that the final result corresponds to one of the provided answer choices.

Now, let's work through each step:

Step 1: We are tasked with multiplying the given decimal number $2.613$ by $100$. In general, multiplying a decimal by a power of ten involves moving the decimal point to the right. When you multiply by $100$, the decimal is moved two places to the right.

Step 2: We begin with the number $2.613$. To multiply by 100, we move the decimal point two places to the right. This results in $261.3$.

Step 3: Now, let's compare our result with the provided choices:

1. $261.6$
2. $261.3$
3. $261$
4. $260.3$

The correct choice, $261.3$, matches our calculated result.

Thus, the solution to the problem is $261.3$.

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

• Step 1: Identify the decimal number provided, which is $1.6$.
• Step 2: Recognize that multiplying by $100$ involves shifting the decimal point two places to the right.

Now, let's apply these steps:

Initially, the number is $1.6$.

Step 2: To multiply by $100$, shift the decimal point from its position between the digits $1$ and $6$ two places to the right. This results in the number $160$.

Thus, by shifting the decimal point two places to the right, $1.6 \times 100$ simplifies to $160$.

Therefore, the solution to the problem is $160$.

To solve this problem, we follow these steps:

• Step 1: Recognize the task is to multiply $1.6$ by $100$.
• Step 2: Determine the number of zeros in $100$, which is $2$.
• Step 3: Move the decimal point in $1.6$ two places to the right.

Let's apply the steps:
When multiplying $1.6$ by $100$, note that there are $2$ zeros in $100$. Hence, move the decimal point in $1.6$ from its original position two places to the right. This transforms $1.6$ to $160$.

Therefore, the product of $1.6$ and $100$ is $160$.

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

• Step 1: Recognize that multiplying a decimal by $100$ requires moving the decimal point two places to the right.
• Step 2: Apply this rule to the given number $2.4$.
• Step 3: Write down the result after performing the operation.

Now, let's work through each step:
Step 1: The number we are multiplying is $2.4$.
Step 2: Since $100$ is $10$ raised to the second power ($10^2$), move the decimal point two places to the right. The number $2.4$ becomes $240$.
Step 3: After moving the decimal, the final result is $240$.

Therefore, the solution to the problem is $240$.

To solve the problem of multiplying $37.1$ by $100$, we can follow these steps:

• Step 1: Understand that multiplying by 100 involves moving the decimal point two places to the right.
• Step 2: Begin with the number $37.1$.
• Step 3: Move the decimal point two places to the right.

Now, let's perform the operation:
- The original number is $37.1$.
- When we move the decimal point two places to the right, $37.1$ becomes $3710.0$.
- For clarity, $3710.0$ is the same as $3710$, as the .0 does not change the value.

Thus, the result of multiplying $37.1 \times 100$ is $3710$.

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

• Step 1: Understand the effect of multiplying a decimal by $100$.

• Step 2: Identify the current position of the decimal point in the number.

• Step 3: Move the decimal point two places to the right.

• Step 4: Compare with the provided choices to identify the correct one.

Now, let's work through each step:
Step 1: Multiplying a number by $100$ involves moving the decimal point two places to the right.
Step 2: The number given is $700.6$. The decimal is currently between the $0$ and $6$.
Step 3: By moving the decimal two places to the right, $700.6$ becomes $70060$.
Step 4: From the choice list, $70060$ matches the answer $70060$.

Therefore, the solution to the problem is $70060$.