Multiplication of Decimal Fractions: Finding the decimal point

To solve this problem, we will place the correct position for the decimal point in the product of $1.35$ and $2.47$.

Let's follow these steps:

• Step 1: Identify the number of decimal places in the numbers being multiplied. $1.35$ has 2 decimal places, and $2.47$ also has 2 decimal places.
• Step 2: Add these decimal places: $2 + 2 = 4$. So, the product should have 4 decimal places.
• Step 3: The given product without considering the decimal point is $33345$. We need to position the decimal so that the product has 4 decimal places.

Now, let's work through applying these steps:
Step 1: $1.35$ and $2.47$ each contribute 2 decimal places.
Step 2: We sum $2 + 2$ to get a total of 4 decimal places for the final result.
Step 3: Place the decimal point in $33345$ so that there are four digits after the decimal point. This gives us $3.3345$.

Therefore, the correct placement of the decimal point in $33345$ is $\mathbf{3.3345}$.

To solve this problem, we'll determine the placement of the decimal point, adhering to the total number of decimal places rule in multiplication:

• Step 1: Identify the decimal places in the numbers.
  - $2.5$ has 1 decimal place.
  - $0.13$ has 2 decimal places.
• Step 2: Calculate the total decimal places in the product:
  - Total: $1 + 2 = 3$ decimal places.
• Step 3: Apply the decimal places to the product $0325$:
  - Insert decimal point into $0325$ such that it reflects 3 decimal places:

Position the decimal to achieve $0.325$.

Therefore, the correct placement of the decimal point results in the answer $\text{0}.325$, matching the given correct answer.

To solve the problem, we need to follow these steps:

• Step 1: Multiply $3.751$ and $0.5$ as though they are whole numbers.
• Step 2: Calculate the product of these whole numbers.
• Step 3: Adjust the decimal point in the product to correspond to the number of decimal places in the original numbers.

Now, let's work through each step:

**Step 1-2**: Multiply $3.751$ by $0.5$ by treating them as $3751$ and $5$. The multiplication is:
$3751 \times 5 = 18755$

**Step 3**: The original numbers have a total of four decimal places (three from $3.751$ and one from $0.5$). Therefore, the result should also have four decimal places. Starting with $18755$, we place the decimal point four places from the right:
$1.8755$

Thus, the correct result with the decimal point placed accurately is $1.8755$.

The correct answer brings us to choice 2: $1.8755$

To resolve the problem of finding the correct decimal point placement in the product of $6.13$ and $2.05$, we proceed as follows:

• Step 1: Calculate the total decimal places by adding the decimal places of each number.
  - The number $6.13$ has 2 decimal places.
  - The number $2.05$ has 2 decimal places.
  - Therefore, the total number of decimal places in the product should be $2 + 2 = 4$.

• Step 2: Place the decimal point in the product number $125665$ to achieve 4 decimal places.
  - Starting from the right, count four places towards the left: $1256.65$.
  - From $1256.65$, adjust to achieve 4 places, resulting in $12.5665$.

Thus, the correctly positioned product is $12.5665$.

In the number -3.5, there is one digit after the decimal point: 5.

In the number 2.4, there is one digit after the decimal point: 4.

In other words, we have two digits after the decimal point.

Therefore we will move the decimal point two places to the left to get our answer: 8.40.

In the number -0.3, there is one digit after the decimal point: 3.

In the number 2.15, there are two digits after the decimal point: 15.

Therefore, we have three digits after the decimal point.

To find the answer, we will count three decimal places to the left, which gives us -0.645.

To solve for the correct placement of the decimal point in the product of $0.05 \times 0.8$, follow these steps:

• Step 1: Convert the multiplication to a format without decimal points by treating the numbers as whole numbers. Multiply $5$ by $8$ to get $40$.
• Step 2: Count the total number of decimal places in the two factors. $0.05$ has 2 decimal places, and $0.8$ has 1 decimal place, summing it up to a total of 3 decimal places.
• Step 3: Position the decimal point in $40$ to achieve 3 decimal places, making it $0.040$.

Thus, the product of $0.05$ and $0.8$ with the decimal point correctly placed is $0.040$.

To solve the problem of finding the correct place for the decimal point in the product $0.10 \times 0.10$, follow these steps:

• Step 1: Identify the number of decimal places in each factor.
• Step 2: Note that $0.10$ has 2 decimal places, and $0.10$ also has 2 decimal places.
• Step 3: Add the decimal places from both factors: $2 + 2 = 4$.
• Step 4: Calculate the product treating them as whole numbers: $10 \times 10 = 100$.
• Step 5: Place the decimal point in the product so that it has a total of 4 decimal places, resulting in $0.0100$.
• Step 6: Simplify $0.0100$ by removing the redundant zeros to get $0.01$.

Therefore, the correct placement of the decimal point in the product $0.10 \times 0.10$ is $0.01$.

To address this problem, we must first carry out the multiplication between $0.2$ and $0.55$, removing the decimals temporarily to simplify the process and then adjust for them correctly in the final product.

Step 1: Convert the decimals to whole numbers.
Rewrite $0.2$ as $2$ (by multiplying by $10$) and $0.55$ as $55$ (by multiplying by $100$).

Step 2: Multiply these whole numbers.
Calculate $2 \times 55 = 110$.

Step 3: Determine where the decimal point should be placed in the result.
- The original number $0.2$ has 1 decimal place.
- The original number $0.55$ has 2 decimal places.
Thus, the total number of decimal places required is $1 + 2 = 3$.

Step 4: Apply these decimal places to the product.
Move the decimal point three places from the right in $110$ to get $0.110$.

Therefore, the correct placement of the decimal point in the product is $0.110$.

Consequently, the choice corresponding to this solution is:$0.110$

To solve this problem, we need to determine the correct position of the decimal point in the product $1413$, which results from multiplying $0.45$ by $3.14$.

• Step 1: Count the decimal places in each factor. The number $0.45$ has 2 decimal places, and $3.14$ has 2 decimal places.
• Step 2: Sum the decimal places from each factor. The total number of decimal places is $2 + 2 = 4$.
• Step 3: Place the decimal point in the result $1413$ such that there are 4 digits following the decimal.

Therefore, the decimal point should be placed to give us $1.413$.

Given the provided choices, the correct option is: $1.413$.

Thus, the corrected and correctly formatted multiplication result is $1.413$.

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

• Step 1: Identify the decimal places in each number.
• Step 2: Determine the total number of decimal places needed in the product.
• Step 3: Adjust the product to include the correct number of decimal places.
• Step 4: Select the correct answer from the choices based on this calculation.

Let's work through these steps:

Step 1: The number $2.35$ has two decimal places, and the number $7.6$ has one decimal place. This gives us a total of $2 + 1 = 3$ decimal places needed in the product.

Step 2: Multiply the numbers as whole numbers: $235 \times 76 = 17860$. Notice it seems like $1786$ in the problem statement, which lacks correct decimal placement.

Step 3: With a total of three decimal places needed in the result, we place the decimal point in $1786$ to make it $17.86$, adding those three decimal places.

Step 4: Compare this with the given options. The placement in option 2 is $\text{\textbf{17.86}}$, which correctly reflects the required three decimal places.

Therefore, the correct solution is \(\textbf{$17.86$}\).

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

• Identify the number of decimal places in each factor
• Sum the decimal places of the factors
• Place the decimal point in the product accordingly
• Confirm with the provided choices

Step 1: Let's determine the decimal places:
The number $2.37$ has 2 decimal places.
The number $1.10$ has 2 decimal places.

Step 2: Calculate the total decimal places:
The sum of the decimal places in both numbers is $2 + 2 = 4$.

Step 3: Position the decimal point in the product:
The result of $2.37 \times 1.10$ is displayed as 2607.
We need to place the decimal point such that the result contains 4 decimal places in total, starting from the rightmost digit.

Step 4: Apply the decimal adjustment:
Starting from the right, place the decimal point 4 places from the right: $2.607$.

Therefore, the correct position of the decimal point in the product is $2.607$.