Division of Decimal Numbers

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 $0.36 \div 0.1$, 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 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 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 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 $7$.