Dividing Decimal Fractions: Long division

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

• Step 1: Recognize that we need to divide $9.6$ by $2$.
• Step 2: Set up the division as you would with whole numbers, keeping in mind the placement of the decimal point.
• Step 3: Divide $9.6$ by $2$ using basic division principles.

Now, let's work through each step:
Step 1: We need to calculate $\frac{9.6}{2}$.
Step 2: Dividing $9$ by $2$, we get $4$ as the quotient, with a remainder of $1$.
Step 3: Bring down the $6$ from the tenth place to make it $16$. Divide $16$ by $2$, resulting in $8$.

Since the decimal is to the right of $9$, it is placed in the result right after $4$, yielding the quotient.
Therefore, the division gives us $4.8$.

The solution to the problem is $4.8$.

To solve the problem of dividing 70.2 by 9, let's perform step-by-step long division:

• Begin with the number 70.2. We treat it as 70 and a fractional part, allowing us to divide separately.
• First, divide 70 by 9 to obtain the integral part of the quotient: $70 \div 9$. Since 9 fits into 70 seven times (as $9 \times 7 = 63$), the integral part is 7.
• Subtract 63 from 70 to get the remainder: $70 - 63 = 7$.
• Now, bring down the decimal part, .2, making it 7.2.
• Divide 7.2 by 9 to obtain the remaining decimal part: $7.2 \div 9 = 0.8$ (since $9 \times 0.8 = 7.2$).
• Add the results: the integral part is 7 and the decimal part is 0.8, making the total quotient 7.8.

Therefore, dividing 70.2 by 9 results in $7.8$, which matches the correct choice.

To solve this problem, follow these steps:

• Step 1: Convert the divisor to a whole number. Multiply 1.5 by 10 to get 15.
• Step 2: Multiply the dividend by the same factor (10) to counterbalance, resulting in 64.5.
• Step 3: Perform the division of whole numbers: $64.5 \div 15$.
• Step 4: Use long division to determine the quotient.

Performing this division:

1. 64.5 divided by 15 is calculated using long division.

2. 15 goes into 64 four times (as $15 \times 4 = 60$). Subtract to get 4.

3. Bring down the next digit (5), making the number 45.

4. 15 goes into 45 exactly three times (as $15 \times 3 = 45$).

5. Subtract to end with 0.

The division results in a quotient of 4.3. Thus, the answer is precisely $4.3$.

Therefore, the correct choice is option 3: 4.3.

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

• Step 1: Eliminate the decimals by multiplying both the numerator (86.4) and the denominator (0.12) by 100. This will convert our division problem to whole numbers: $\frac{8640}{12}$.
• Step 2: Perform the division $8640 \div 12$.

Now, let's execute these steps.

Step 1: Multiply 86.4 by 100 to get 8640 and 0.12 by 100 to get 12. Our division problem is transformed to $\frac{8640}{12}$.

Step 2: Perform the division:

Long Division of 8640 by 12:

• 12 goes into 86 seven times since $12 \times 7 = 84$. Subtract to get 2.
• Bring down the next digit (4), making it 24. 12 goes into 24 exactly twice since $12 \times 2 = 24$. Subtract to get 0.
• Bring down the final digit (0), making it 0. 12 goes into 0 zero times.

The quotient from the calculation is 720.

Therefore, the solution to the problem is $720$.

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

• Step 1: Eliminate decimal points by adjusting the numbers.
• Step 2: Apply long division to the resulting numbers.
• Step 3: Precisely place the decimal in the final result.

Now, let's apply these steps:

Step 1: Convert both numbers to eliminate decimals.
Multiply both $70.62$ and $3.3$ by $10$ to give $706.2$ and $33$, respectively, for simplicity.

Step 2: Perform the long division of $706.2$ by $33$, following regular long division steps:
- Divide $70$ by $33$, which gives approximately $2$. Write down $2$ and multiply $2 \times 33 = 66$.
- Subtract $66$ from $70$ to get $4$. Bring down the next digit, $6$, making it $46$.
- Divide $46$ by $33$ gives approximately $1$. Write down $1$ and multiply $1 \times 33 = 33$.
- Subtract $33$ from $46$ to get $13$. Bring down $2$ to make $132$.
- Divide $132$ by $33$ gives exactly $4$. Write down $4$ and $4 \times 33 = 132$.
- Subtract $132$ from $132$ results in $0$.

Step 3: Placement of the decimal point.
Since we adjusted both numbers by multiplying by $10$, the effect cancels out. The final quotient is $21.4$.

Therefore, the solution to the problem is $21.4$.

To solve this problem, let's break it down into specific steps:

• Step 1: Identify the given values. We have two significant numbers: $2.5$ represents a whole while $0.3350$ is likely to represent a section related to the total.
• Step 2: Determine the ratio or part-to-whole relation. In a simple comparison or fraction, $0.3350$ of the full length represented as a percentage needs to be interpreted.
• Step 3: Recognize that $0.3350$ can be approximated to $0.335$; we aim to find how this properly translates into the correct standardized decimal form compared next to the whole.
• Step 4: Simplify to nearest correct clearest fraction based on context, thus making it $\frac{0.335}{2.5 + 0.335}$.

However here, the task might include interpreting the label to safely imply needing translation out of these choices provided (considering errors in potential context). Thus, to simplify:
Comparatively, direct foundational calculations do assuredly guide us translating closer to $0.134$ alongside what mathematical choices are prescribed.

Therefore, the solution to the problem in standardized form, given the nearest descriptive choice, is $0.134$.

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

• Step 1: Identify the given numbers: 23.828 and 0.28.
• Step 2: Perform division: Divide 23.828 by 0.28.
• Step 3: Compare the result with the given choices.

Now, let's work through each step:
Step 1: We have the numbers 23.828 and 0.28.
Step 2: Perform the division $23.828 \div 0.28$.

To divide 23.828 by 0.28:
- Move the decimal point in the divisor (0.28) two places to the right to make it a whole number (28).
- Move the decimal point in the dividend (23.828) the same number of places to the right, resulting in 2382.8.
- Now, divide 2382.8 by 28 using a calculator or long division method: $2382.8 \div 28 = 85.1$.

Therefore, the result of dividing 23.828 by 0.28 is $85.1$.

This matches option 3, with the correct choice being 85.1.