Multiplication of Decimal Fractions - Examples, Exercises and Solutions

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 $\mathbf{3.3345}$.

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 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 $0.0045$.