Dividing Decimal Fractions - Examples, Exercises and Solutions

To solve the division of decimals $0.49 \div 0.1$, follow these steps:

• Step 1: Start by identifying the dividend ($0.49$) and the divisor ($0.1$).
• Step 2: To simplify the division process, eliminate the decimal in the divisor. Multiply both the dividend and the divisor by 10. This gives: $(0.49 \times 10) \div (0.1 \times 10) = 4.9 \div 1$.
• Step 3: Perform the simple division with the new values: $4.9 \div 1 = 4.9$.

Therefore, the result of $0.49 \div 0.1$ is $4.9$.

To solve the problem $0.7 \div 0.1$, we proceed with the following steps:

• Step 1: Convert the decimals to whole numbers. Multiply both $0.7$ and $0.1$ by 10 to remove the decimals. This gives us $7$ and $1$ respectively.
• Step 2: Divide the resulting whole numbers. Hence, $7 \div 1 = 7$.
• Step 3: The division is straightforward as the divisor is now a whole number.

Therefore, the solution to the problem is $7$.

To solve the problem of $1.3 \div 0.1$, we need to simplify the division process by eliminating the decimal point in the divisor using the following steps:

• Step 1: Recognize that dividing by 0.1 is equivalent to multiplying by 10. This is because 0.1 is the same as $\frac{1}{10}$, so dividing by 0.1 is the same as multiplying by 10.
• Step 2: Multiply both the dividend (1.3) and the divisor (0.1) by 10 to move the decimal point one place to the right for each number. This changes 1.3 to 13 and 0.1 to 1.
• Step 3: Perform the division $13 \div 1$. As dividing by 1 leaves any number unchanged, we have the result 13.

Therefore, the solution to the problem $1.3 \div 0.1$ is $13$.

To solve the division of two decimal numbers, we start by converting the divisor, 0.1, into a whole number to simplify the calculation.

• Step 1: Multiply both the dividend and the divisor by 10 to eliminate the decimal in the divisor. This gives us:

$3.36 \times 10 = 33.6$ and $0.1 \times 10 = 1$

• Step 2: The division is now transformed from $\frac{3.36}{0.1}$ to $\frac{33.6}{1}$.

Step 3: Dividing 33.6 by 1 results simply in 33.6.

There's no change needed to any number beyond this step, as the division by 1 does not alter the value.

Therefore, the solution to the problem is $33.6$.

To solve the problem $0.36 \div 0.1$, we use the method of converting to whole numbers as follows:

• Step 1: Multiply both 0.36 and 0.1 by 10 to get rid of the decimals. This gives us $3.6$ and $1$.
• Step 2: Perform the division of $3.6$ by $1$, which simply results in $3.6$.

Thus, the result of $0.36 \div 0.1$ is $3.6$.

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

• Step 1: Identify the division operation: $4.2 \div 0.1$.
• Step 2: Convert the operation into a simpler form by eliminating decimals from the divisor.
• Step 3: Multiply both the dividend $4.2$ and the divisor $0.1$ by 10 to shift the decimal point.
• Step 4: After multiplying, the operation becomes $42 \div 1$.
• Step 5: Calculate the result of $42 \div 1$, which equals 42.

Now, let’s work through the solution with respect to each step:

Step 1: We recognize the operation is $4.2 \div 0.1$. This indicates we need to divide 4.2 by 0.1.

Step 2: To facilitate easier calculation, we aim to eliminate the decimal in the divisor. We can achieve this by multiplying 0.1 by 10, turning it into the whole number 1.

Step 3: When we multiply the divisor $0.1$ by 10, we must do the same to the dividend $4.2$ to maintain the equality of the operation. Multiplying 4.2 by 10 shifts its decimal point one position to the right, resulting in 42.

Step 4: The division now reads $42 \div 1$. This is straightforward since dividing any number by 1 gives the number itself.

Step 5: Therefore, calculating $42 \div 1$, we find that the result is 42.

Consequently, the solution to the problem is $42$.

To solve the problem of dividing the decimal numbers $0.412$ by $0.01$, we'll simplify the division by eliminating the decimal points:

• Step 1: Recognize that dividing by a decimal can be simplified by converting both the dividend and the divisor to whole numbers.
• Step 2: Multiply both $0.412$ and $0.01$ by $100$ to make both numbers integers:
• $0.412 \times 100 = 41.2$
• $0.01 \times 100 = 1$
• Step 3: The division $0.412 \div 0.01$ simplifies to $41.2 \div 1$.
• Step 4: Dividing $41.2$ by $1$ gives a result of $41.2$.

Therefore, the solution to the problem is $41.2$.

The task is to divide $0.121$ by $0.1$.

To simplify this calculation, we can eliminate the decimal in the divisor:

• Multiply both the dividend and the divisor by 10:

$0.121 \times 10 = 1.21$

$0.1 \times 10 = 1$

Now we divide $1.21$ by $1$, which simplifies to:

$1.21 \div 1 = 1.21$

Thus, the answer to the division $0.121 \div 0.1$ is $1.21$.

Matching this result with the provided choices, the correct answer is:

• $1.21$, which corresponds to choice 3.

Therefore, the solution to the problem is $1.21$.

To solve this problem, we'll adopt the following approach:

• Step 1: Multiply both numbers by 100 to simplify the division.
• Step 2: Perform the division on whole numbers.

Now, let's work through the steps:
Step 1: Multiplying $0.7$ by 100, we obtain $70$. Multiplying $0.01$ by 100, we obtain $1$.
Step 2: Now perform the division: $70 \div 1 = 70$.

Therefore, the solution to the problem is $70$.

To solve this problem, follow these steps:

• Step 1: Recognize that you are required to divide $3.3$ by $0.01$.
• Step 2: Multiply both the dividend and the divisor by 100 to remove decimals for easier computation.
• Step 3: Calculate $3.3 \times 100 = 330$ and $0.01 \times 100 = 1$.
• Step 4: Now perform the division: $330 \div 1 = 330$.

This shows that when $3.3$ is divided by $0.01$, it results in $330$.

Therefore, the solution to the problem is $330$.

To solve the problem $0.36 \div 0.01$, we follow these steps:

• Firstly, to simplify this division with decimals, we will eliminate the decimals by converting them to whole numbers. We can do this by multiplying both numbers by 100.
• Multiply $0.36$ by 100: $0.36 \times 100 = 36$.
• Multiply $0.01$ by 100: $0.01 \times 100 = 1$.
• Now, our expression simplifies to dividing whole numbers: $36 \div 1 = 36$.

Therefore, the solution to the division $0.36 \div 0.01$ is $36$.

To solve the division $4.2 : 0.01$, follow these steps:

• Step 1: Recognize that dividing by a smaller decimal like $0.01$ is equivalent to multiplying by 100, since $0.01 = \frac{1}{100}$.
• Step 2: Convert $4.2$ and $0.01$ to whole numbers by multiplying both by 100. This results in $420$ and $1$ respectively.
• Step 3: Perform division with the whole numbers: $\frac{420}{1} = 420$.

Therefore, by dividing $4.2$ by $0.01$ and adjusting the decimal places, we find the result is $420$.

To solve the problem of dividing $1.1$ by $0.5$, let's simplify the operation by converting the decimals into whole numbers:

• Step 1: Multiply both the dividend and the divisor by $10$ to eliminate the decimal points:
  $1.1 \times 10 = 11$
  $0.5 \times 10 = 5$

• Step 2: Perform division on the whole numbers:
  $11 \div 5 = 2.2$

• Step 3: Interpret the result. We found that the answer to the division $1.1 \div 0.5 = 2.2$.

Therefore, the solution to the problem is $2.2$.

To solve the problem $0.4 \div 0.2$, we can follow these steps:

• Step 1: Convert the division of decimals into a division of whole numbers by multiplying both the dividend (0.4) and the divisor (0.2) by 10.
• Step 2: This operation results in dividing 4 by 2 (since $0.4 \times 10 = 4$ and $0.2 \times 10 = 2$).
• Step 3: Perform the division $4 \div 2$, which equals 2.

Thus, the result of dividing $0.4$ by $0.2$ is $\boxed{2}$.

To solve the problem $0.1 \div 0.02$, let's follow these steps:

• Step 1: Eliminate the decimals by multiplying both the dividend and divisor by 100 to convert them to whole numbers.
• Step 2: Convert $0.1$ to $10$ and $0.02$ to $2$ by multiplication.
• Step 3: Perform the division $10 \div 2$.

Now, let's proceed with the calculations:
- When we multiply $0.1$ by 100, we get $10$. Similarly, multiplying $0.02$ by 100 gives us $2$.
- Next, we divide $10$ by $2$:
$10 \div 2 = 5$.

Therefore, the solution to the problem is $5$.