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

To solve the problem of dividing 100.1 by 100, we will perform the following steps:

• Step 1: Identify the starting position of the decimal point in 100.1, which is 1 place after the first zero, i.e., between 100 and 1.
• Step 2: Move the decimal point two places to the left because we are dividing by 100. The first move places the decimal point before '0', and the second move places it before '1'.
• Step 3: Now, add zeros if needed to the front to denote the newly formed decimal number.

After moving the decimal, 100.1 becomes 1.001. This is the result of dividing 100.1 by 100. Therefore, the solution to the problem is:

$1.001$

To solve this division problem, we need to divide the number 33631 by 100. This can be efficiently accomplished by shifting the decimal point two positions to the left, given the rule of dividing by powers of 10.

Let's follow this step-by-step:

• Step 1: Recognize that 33631 as a whole number can be rewritten as 33631.0, indicating the implicit decimal point.
• Step 2: For division by 100, shift the decimal point two places to the left.

Routinely executing this: 33631.0 becomes 336.31, as the decimal point shifts two positions to the left.

Thus, after dividing 33631 by 100, the result is $336.31$.

To solve $2101 \div 100$, we proceed as follows:

Step 1: Understand the effect of dividing by 100. Dividing by 100 means moving the decimal point two spaces to the left in the number 2101.

Step 2: Initially, 2101 can be thought of as 2101.0 for ease of manipulation, even though it is a whole number.

Step 3: Shift the decimal two places to the left.

• Originally: 2101.0
• First shift: 210.10 (Moving one place)
• Second shift: 21.01 (Moving the second place)

Thus, the number after division is 21.01. Therefore, the result of $2101 \div 100$ is $21.01$.

Consequently, the solution to the problem is $21.01$.

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

• Step 1: Understand the given information and operation.
• Step 2: Apply the rule for division by 100.
• Step 3: Perform the calculation and check against the choices.

Now, let's work through each step:

Step 1: We need to divide 1036 by 100. This is equivalent to finding how many hundreds fit into 1036.

Step 2: When dividing a number by 100, the decimal point is shifted two positions to the left. The original number 1036 can be expressed as 1036.0 (adding a decimal point and a zero for clarity). By moving the decimal point two places to the left, we convert 1036.0 to 10.36.

Step 3: Therefore, $1036 \div 100 = 10.36$.

Comparing this result to the given multiple-choice options, the correct answer is choice 2, which is $10.36$.

Therefore, the solution to this problem is $10.36$.

To solve this problem of dividing 124 by 100, we apply the following procedure:

• Step 1: Recognize that the number 124 can be simplified in our problem by considering it with a decimal for ease, $124 = 124.0$.
• Step 2: Understand that dividing by 100 means moving the decimal point two places to the left.
• Step 3: Move the decimal point from its original position (at the end of 124.0) to two places to the left. After sliding the decimal point, $124.0$ becomes $1.24$.

Hence, when we divide 124 by 100, the resulting number is $1.24$.

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

• Step 1: Understand the concept of dividing by 100
• Step 2: Apply this concept to 1.100 by moving the decimal point two places to the left
• Step 3: Verify the final answer against the choices provided

Now, let's work through each step:

Step 1: When dividing a number by 100, move the decimal point two places to the left. This is because 100 is $10^2$, so we shift the decimal point by two places.

Step 2: Starting with the number 1.100, we move the decimal point two places to the left. The decimal point moves as follows:

• The original number is $1.100$.
• Moving the decimal one place to the left gives $0.1100$.
• Moving the decimal another place to the left results in $0.01100$.

Thus, moving two places gives us $0.01100$, which is equivalent to $0.011$ when removing trailing zeros.

Step 3: We check our work against the answer choices:

1. $0.01$
2. $0.11$
3. $0.011$
4. $0.1$

The correct solution $0.011$ corresponds to choice 3.

Therefore, the solution to the problem is $0.011$.

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

• Step 1: Identify the current position of the decimal point.
• Step 2: Move the decimal point two places to the left, as we are dividing by 100.

Now, let's work through the calculation:

Step 1: The number 231 is actually 231.0 when viewed as a decimal.

Step 2: Since we are dividing by 100, we move the decimal point two places to the left:
Starting from 231.0, moving two places left gives us 2.31.

Therefore, the solution to the problem is $2.31$.

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

• Step 1: Interpret the division operation and use it.
• Step 2: Apply the division method by shifting the decimal.

Now, let's work through each step:
Step 1: The problem gives us the division operation $12:100$. We can represent this as $\frac{12}{100}$ or $12 \div 100$.
Step 2: When we divide 12 by 100, we shift the decimal point of 12 two places to the left. The number 12 can be written as 12.0 (with an implied decimal point), so shifting two places gives us 0.12.

Therefore, the result of $12:100$ is $0.12$.

To solve this problem, we need to divide $118$ by $100$. To do this, we'll use the method of moving the decimal point.

The number $118$ can be expressed as $118.0$ with an implied decimal point at the end. When dividing by $100$, which is $10^2$, we move the decimal point two places to the left to find the quotient.

• First Place: $118.0 \to 11.80$
• Second Place: $11.80 \to 1.180$

After moving the decimal two places to the left, the result becomes $1.18$.

Therefore, the solution to the problem is $1.18$.

To solve the division of $9.19$ by 100, we follow these steps:

• Identify the initial position of the decimal point in $9.19$.
• Move the decimal point two places to the left since we are dividing by 100.
• Record the resulting number.

Let's work through this:

Original number: $9.19$

Step 1: Current position of the decimal in $9.19$ is between 9 and 1.

Step 2: Move the decimal two places to the left:

- First move: From between 9 and 1 to before 9, it becomes $0.919$

- Second move: Insert an extra 0 to the left, resulting in $0.0919$

Therefore, the result of $9.19 \div 100$ is $\mathbf{0.0919}$.

The correct choice matches the calculated result, which confirms choice $2$: $\mathbf{0.0919}$.

To solve the problem of dividing $10$ by $100$, we'll follow these steps:

• Recognize the task as a division by 100.
• Understand that dividing by 100 effectively moves the decimal point two places to the left.
• Apply this understanding directly to the number $10$.

Let's work through these steps:

The number $10$ can be written as $10.0$, and dividing by $100$ means moving the decimal point two places to the left.
So, starting with $10.0$, we move the decimal:

$\text{Before: } 10.0$

$\text{After moving the decimal two places left: } 0.10$

Thus, $10:100 = 0.1$.

The correct answer is therefore: $0.1$.

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

• Step 1: Start with the number 1, which can be written as $1.00$.

• Step 2: Since dividing by 100 is involved, we move the decimal point two places to the left, resulting in 0.01.

• Step 3: Identify the answer from the given choices.

Now, let's work through each step:
Step 1: Write the number 1 in decimal form as 1.00.
Step 2: Divide by 100 by moving the decimal point two places to the left.
- Moving one place to the left gives 0.10.
- Moving another place to the left gives 0.01.
Step 3: The resulting value is 0.01, which corresponds to choice 2.

Therefore, the solution to the problem is $0.01$.

To solve the division of $15.5$ by $100$, we follow these steps:

• Step 1: Identify the position of the decimal point in $15.5$. Initially, the decimal point is just after the digit $15$.
• Step 2: Move the decimal point two places to the left. This is because dividing by $100$ shifts the decimal to the left by two places. Thus, $15.5$ becomes $0.155$.

Therefore, the result of $15.5 \div 100$ is $\boxed{0.155}$.

To solve the problem of dividing 1.55 by 100, follow these steps:

• Step 1: Understand that dividing by 100 means moving the decimal point two places to the left.
• Step 2: Start with the number 1.55. The decimal is currently between the 1 and the 5.
• Step 3: Move the decimal point two places to the left. The first move takes it in front of the 1, making it 0.155. The second move places it to the left of the 0, resulting in 0.0155.

Therefore, when you divide 1.55 by 100, the result is $0.0155$.

Given the available choices, the correct choice is choice 3: $0.0155$.

Therefore, the solution to the problem is $0.0155$.

To solve this problem, we'll divide 13 by 100 using the movement of the decimal point method:

• Step 1: Convert the integer 13 to a decimal by considering it as 13.0. This highlights the position where the decimal point begins.
• Step 2: Since we are dividing by 100, we need to move the decimal point two places to the left. Starting with 13.0:
• First move one place left: 1.30
• Second move one place left: 0.130
• Step 3: Thus, the final representation after moving two places to the left is 0.13.

Therefore, when dividing 13 by 100, the resulting decimal number is $0.13$.

The correct answer from the given choices is choice (3), which is $0.13$.

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

• Step 1: Identify the given information, which is the number 1.2 and that we need to divide it by 100.
• Step 2: Recognize that dividing by 100 means moving the decimal point in 1.2 two places to the left.
• Step 3: Shift the decimal point two places to the left in 1.2, resulting in 0.012.

Now, let's work through this solution in detail:

Step 1: We begin with the number 1.2.
Step 2: To divide by 100, visualize the decimal point moving two places left. Since 1.2 is represented as 1.2 (or 1.20 for easier visualization), the decimal point moves past the "1" and an extra zero is added in front:
- Original: 1.2
- First move: 0.12
- Second move: 0.012

Therefore, the solution to the problem is $0.012$.

To solve the problem of dividing $62.35$ by $100$, we need to understand how dividing by powers of ten affects a decimal. Dividing by $100$ is equivalent to shifting the decimal point two places to the left.

Let's follow these steps to find our solution:

• Step 1: Identify the original decimal: $62.35$.

• Step 2: Since we are dividing by $100$, shift the decimal point two places to the left:

Starting with $62.35$, the decimal point is currently after the $2$. Moving it two places to the left gives us: $\begin{aligned} Initial: & \quad 62.35\\ Shift~one~place: & \quad 6.235\\ Shift~two~places: & \quad 0.6235 \end{aligned}$

Therefore, the result of dividing $62.35$ by $100$ is $0.6235$.

Examining the choices, the correct answer is clearly choice (2): $0.6235$.

Thus, the solution to the problem is $\boxed{0.6235}$.

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

• Step 1: Identify the given information
• Step 2: Perform the division by shifting the decimal
• Step 3: Determine the correct answer choice

Now, let's work through each step:
Step 1: We are given $15.2$ and need to divide by $100$.
Step 2: Since dividing by $100$ involves moving the decimal point two places to the left, we take $15.2$ and shift the decimal to get $0.152$.
Step 3: Comparing our result with the answer choices, $0.152$ corresponds to choice id $3$.

Therefore, the solution to the problem is $0.152$.