Multiplication of Decimal Fractions: Multiplication by tenths or hundredths

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 the multiplication of $0.01 \times 0.101$, follow these steps:

• Step 1: Consider both numbers without decimals as whole numbers. Here, interpret $0.01$ as $1$ and $0.101$ as $101$.
• Step 2: Multiply these whole numbers: $1 \times 101 = 101$.
• Step 3: Count the number of decimal places in each factor. For $0.01$, there are 2 decimal places. For $0.101$, there are 3 decimal places, totaling $2 + 3 = 5$ decimal places in the product.
• Step 4: Insert a decimal point in the integer product of $101$ to give it 5 decimal places. Starting from the right of the number, move the decimal point 5 places to the left, yielding $0.00101$.

Thus, the correct answer is $\mathbf{0.00101}$, which corresponds to choice $\mathbf{3}$.

To solve this problem, we'll use the following steps:

• Step 1: Multiply the numbers as if they were whole numbers.
• Step 2: Count the number of decimal places in the original numbers.
• Step 3: Position the decimal point in the product accordingly.

Let's go through each step in detail:
Step 1: Multiply $1 \times 300 = 300$.
Step 2: Count the decimal places: $0.01$ has 2 decimal places and $0.300$ has 3 decimal places, making a total of 5 decimal places.
Step 3: Place the decimal point in the result 300, counting 5 places from the right: $0.00300$ (we can drop the trailing zeros to write it as $0.003$).

Therefore, the solution to the problem is $0.003$.

To solve the problem $0.01 \times 0.315$, we'll follow these steps:

• Step 1: Multiply the numbers ignoring the decimal points.
• Step 2: Place the decimal point in the product according to the combined decimal places in the original numbers.

Let's proceed through each step:

First, multiply the numbers as whole numbers: $1 \times 315 = 315$.

Next, count the total number of decimal places in the factors. The number $0.01$ has two decimal places, and $0.315$ has three decimal places, adding up to five decimal places.

Therefore, in the product, we need to place the decimal point five places from the right.

Starting from $315$, we place the decimal point to get $0.00315$. Since we add three leading zeros to accommodate the five decimal places total.

Thus, the result of $0.01 \times 0.315$ is $0.00315$.

To solve this problem, follow these steps:

• Step 1: Multiply the numbers without considering the decimals. Calculate $1 \times 50 = 50$.
• Step 2: Count the total number of decimal places in both original numbers. $0.01$ has two decimal places, and $0.50$ has two decimal places. This gives a total of four decimal places.
• Step 3: Apply the total number of decimal places to the whole number product from Step 1. Therefore, $50$ becomes $0.005$.

Thus, the calculation shows that $0.01 \times 0.50 = 0.005$.

Therefore, the solution to the problem is $\textbf{0.005}$.

To solve this multiplication problem, we will follow these steps:

• Step 1: Convert both decimal numbers to fractions or remove the decimals by considering them as whole numbers.
• Step 2: Multiply these whole numbers.
• Step 3: Place the decimal in the resulting product correctly by counting the sum of the decimal places in the original numbers.

Now, let's work through each step:

Step 1: We have the numbers $0.01$ and $0.45$.
Convert $0.01$ to $\frac{1}{100}$ and $0.45$ to $\frac{45}{100}$.

Step 2: Multiply $\frac{1}{100} \times \frac{45}{100} = \frac{1 \times 45}{100 \times 100} = \frac{45}{10000}$.

Step 3: Convert $\frac{45}{10000}$ back to a decimal form. Since $10000$ has 4 zeros, move the decimal four places to the left: $0.0045$.

Therefore, the product of $0.01$ and $0.45$ is $0.0045$.

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

• Step 1: Multiply $0.01$ by $285.11$ considering decimal multiplication rules.
• Step 2: Determine the placement of the decimal point in the product.
• Step 3: Identify the correct answer choice based on the calculation.

Now, let's work through each step:

Step 1: First, convert the numbers into whole numbers and multiply:

$0.01 = \frac{1}{100}$ and $285.11 = 28511/100$.

Ignoring the decimals temporarily, calculate $1 \times 28511 = 28511$.

Step 2: Determine the placement of the decimal point:

Since $0.01$ has 2 decimal places and $285.11$ has 2 decimal places, the total number of decimal places in the product is $2 + 2 = 4$.

Adjust the product $28511$ by placing the decimal point 4 places from the end:

This gives us $2.8511$.

Step 3: Compare this result with the given choices.

The correct answer is the choice that matches our calculation:

The solution to the problem is $2.8511$.

The task is to find the product of two decimal numbers: $0.01$ and $3.5$. Follow these steps to compute the product:

• Step 1: Remove the decimal points and multiply as if they are whole numbers. Multiplying $1$ by $35$ gives $35$.
• Step 2: Count the total number of decimal places in both decimal numbers. The number $0.01$ has 2 decimal places, and $3.5$ has 1 decimal place, for a total of 3 decimal places.
• Step 3: Place the decimal point in the product so that the result has the same total number of decimal places counted in step 2. Thus, $35$ becomes $0.035$.

Following these steps ensures the decimal point is positioned correctly, resulting in the product $0.035$.

Therefore, the solution to the problem is $0.035$.

To solve the problem of multiplying $0.01$ by $44.9$, we follow these steps:

• Step 1: Convert numbers to eliminate decimals. Multiply $1$ by $449$ (as $0.01 = \frac{1}{100}$ and $44.9 = \frac{449}{10}$).

• Step 2: Perform the multiplication $1 \times 449$, which equals $449$.

• Step 3: Adjust for decimal places. Since there are three decimal places combined in $0.01$ and $44.9$ (two from $0.01$ and one from $44.9$), the result $449$ should have three decimal places.

The correct placement of the decimal point gives us $0.449$.

Therefore, the solution to the problem is $\mathbf{0.449}$.

To solve this problem, we'll multiply the decimal numbers $0.01$ and $4.8$.

Here's how we can approach this:

• Step 1: Identify the number of decimal places.
  - $0.01$ has two decimal places.
  - $4.8$ has one decimal place.
  - Total decimal places in the product will be $2 + 1 = 3$.
• Step 2: Multiply the numbers as whole numbers, ignoring the decimal point.
  Multiply $1$ (from $0.01$) by $48$ (from $4.8$): $1 \times 48 = 48$.
• Step 3: Place the decimal point in the product.
  Given that there are three decimal places in total, the product $48$ becomes $0.048$.

Therefore, the solution to the problem is $0.048$.

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

• Step 1: Multiply the numbers as if they were whole numbers.
• Step 2: Count the total number of decimal places in both the numbers and place the decimal point in the product accordingly.

Now, let's work through each step:
Step 1: Multiply $55.31$ by $1$, which gives $55.31$.
Step 2: Since $0.01$ has 2 decimal places, moving the decimal place in $55.31$ two places to the left gives us $0.5531$.

Therefore, the solution to the problem is $0.5531$, which corresponds to choice $3$.

To solve this problem, follow these steps:

• Step 1: Temporarily ignore the decimals and multiply $1$ by $24$. The product is $24$.
• Step 2: Count the decimal places in both numbers. $0.1$ has one decimal place, and $2.4$ has one decimal place. This gives a total of two decimal places.
• Step 3: Place the decimal point in the product, which is $24$, to account for the two decimal places. Thus, $24$ becomes $0.24$.

Therefore, the solution to the problem $0.1 \times 2.4$ is $0.24$.

To solve the problem of finding $0.1 \times 33.4$, we'll employ the following method:

• Step 1: Multiply the numbers without considering decimals.
  Calculate $1 \times 33.4 = 33.4$.
• Step 2: Determine the decimal placement.
  The number $0.1$ has one decimal place, and $33.4$ has one decimal place. Therefore, the product should have $1 + 1 = 2$ decimal places.
• Step 3: Apply the decimal adjustment.
  Take the product $33.4$ and insert two decimal places from the right. This results in $3.34$.

Thus, the solution to the problem $0.1 \times 33.4$ is $\mathbf{3.34}$.

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

• Step 1: Multiply the numbers without considering the decimal point.
• Step 2: Count the total number of decimal places in the numbers being multiplied.
• Step 3: Position the decimal point in the product accordingly.

Now, let's work through each step:

Step 1: Multiply $0.1$ by $3.5$ as whole numbers $1 \times 35 = 35$.

Step 2: Count the decimal places: $0.1$ has 1 decimal place, and $3.5$ has 1 decimal place, totaling 2 decimal places.

Step 3: In the product $35$, place the decimal point such that there are 2 decimal places: This gives us $0.35$.

Therefore, the solution to the problem is $0.35$.

Let's solve the problem of multiplying $0.1$ and $7.33$ step by step.

Step 1: Rewrite the two numbers without considering the decimal points. Calculate the product of 10 and 733.

Step 2: The result of $10 \times 733$ is $7330$.

Step 3: Count the total number of decimal places in the original factors $0.1$ and $7.33$.
- $0.1$ has 1 decimal place.
- $7.33$ has 2 decimal places.
Together, they amount to 3 decimal places.

Step 4: In the product $7330$, move the decimal point backwards to account for the 3 decimal places. So, the decimal point goes three places from the end of the number.

The result is $0.733$.

Therefore, $0.1 \times 7.33 = 0.733$.

The correct answer choice is $0.733$.

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

• Identify and Analyze Decimal Places: Both numbers $0.1$ and $74.8$ have decimal points. Specifically, $0.1$ has one decimal place, and $74.8$ has one decimal place, making a total of two decimal places.
• Perform Multiplication: Multiply the numbers as if they were whole numbers. Ignoring decimal points, multiply $1 \times 748$, which equals $748$.
• Place the Decimal Point: Since the multiplication involves two decimal places in total (one from each factor), the product $748$ should be adjusted to have two decimal places. Thus, it becomes $7.48$.

Thus, the result of multiplying $0.1 \times 74.8$ is $\mathbf{7.48}$.

The correct answer is choice 2: $\mathbf{7.48}$.