Multiplication of Decimal Numbers

To solve this problem, we'll multiply the decimals as follows:

• Step 1: Multiply the whole numbers 1 and 4. This gives us 4.
• Step 2: Count the total number of decimal places in the factors. $0.1$ has 1 decimal place, and $0.004$ has 3 decimal places.
• Step 3: In the final answer, place the decimal point to ensure our product has $1 + 3 = 4$ decimal places.

Now, let's apply these steps:

First, multiply 1 by 4 to get 4. Then place the decimal in the product so it has 4 decimal places: $0.0004$.

Therefore, the solution to the problem is $0.0004$.

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

• Step 1: Convert the decimal numbers into a form that is easier to multiply.
• Step 2: Multiply the numbers as if they were whole numbers.
• Step 3: Adjust the product by placing the decimal point correctly.

Now, let's work through each step:

Step 1: Convert the decimals $0.1$ and $0.35$ into whole number expressions:

• $0.1$ can be thought of as $\frac{1}{10}$.
• $0.35$ can be thought of as $\frac{35}{100}$.

Step 2: Multiply as whole numbers: Multiply $1$ and $35$ to obtain $35$.

Step 3: Adjust the decimal point:

• $0.1$ has 1 decimal place.
• $0.35$ has 2 decimal places.

Therefore, the product of $0.1$ and $0.35$ is $0.035$.

Looking at the choices provided:

• Choice 1: $0.35$ is incorrect as it does not consider the decimal adjustment.
• Choice 2: $0.035$ is correct.
• Choice 3: $0.350$ is incorrect as it has an extra zero and maintains the incorrect placement of the decimal point.
• Choice 4: $0.310$ is incorrect as it does not correspond with the straightforward multiplication of the operands.

Thus, the correct choice is $0.035$.

To solve this problem, we'll multiply the decimal numbers $0.1$ and $0.5$, following these steps:

• Step 1: Treat each number as if it were a whole number and multiply: $1 \times 5 = 5$.
• Step 2: Count the decimal places in both factors. The number $0.1$ has one decimal place, and $0.5$ also has one decimal place.
• Step 3: The total number of decimal places in the product should be the sum of the decimal places in the factors, which is $1 + 1 = 2$.
• Step 4: Place the decimal point in the product $5$, resulting in $0.05$, to ensure it has two decimal places.

Therefore, the product of $0.1$ and $0.5$ is $0.05$.

To solve $0.1 \times 0.999$, we need to follow these steps carefully:

• Step 1: Treat the numbers as integers and multiply them. Ignoring the decimal points temporarily, multiply $1$ by $999$:
  $\quad 1 \times 999 = 999$.
• Step 2: Determine the total number of decimal places in the factors.
  $\quad 0.1$ has 1 decimal place.
  $\quad 0.999$ has 3 decimal places.
  Therefore, the product should have $1 + 3 = 4$ decimal places.
• Step 3: Position the decimal in the product calculated in step 1.
  $\quad 999$ with 4 decimal places becomes $0.0999$.

Therefore, the product of $0.1 \times 0.999$ is $0.0999$.

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 $\mathbf{3.3345}$.