To divide \( 754 \div 1200 \) using the long division method, follow these steps:

### Step 1: Setup the division
We want to divide 754 by 1200. Since 1200 is larger than 754, the whole number part of the quotient will be zero, so we’ll move on to decimal places.

### Step 2: Add decimal point and zeros
- Place a decimal point after the 754, and add zeros to continue the division.
- We will calculate up to three decimal places for accuracy.

We are essentially calculating \( 754.000 \div 1200 \).

### Step 3: Perform long division

1. **How many times does 1200 go into 754?**  
   - 1200 doesn't go into 754, so write 0 in the quotient.
   - Add a decimal point and bring down the next digit (0), making it 7540.

2. **How many times does 1200 go into 7540?**  
   - \( 7540 \div 1200 \approx 6 \), so 6 is the next digit in the quotient.
   - Multiply \( 6 \times 1200 = 7200 \).  
   - Subtract \( 7540 - 7200 = 340 \).

3. **Bring down the next 0** to make it 3400.

4. **How many times does 1200 go into 3400?**  
   - \( 3400 \div 1200 \approx 2 \), so 2 is the next digit.
   - Multiply \( 2 \times 1200 = 2400 \).
   - Subtract \( 3400 - 2400 = 1000 \).

5. **Bring down the next 0** to make it 10000.

6. **How many times does 1200 go into 10000?**  
   - \( 10000 \div 1200 \approx 8 \), so 8 is the next digit.
   - Multiply \( 8 \times 1200 = 9600 \).
   - Subtract \( 10000 - 9600 = 400 \).

Thus, the division yields \( 0.628 \) (rounded to three decimal places).

### Final Answer:
\[ 754 \div 1200 = 0.628 \]

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Would you like more details or further explanation?

Here are 5 related questions to explore:

1. How does long division work with larger decimals?
2. Can we simplify \( 754 \div 1200 \) into a fraction?
3. What is the process for dividing two large numbers without using decimals?
4. How can you estimate quotients when dividing complex numbers?
5. What is the relationship between long division and real-world applications?

**Tip:** Always add zeros after the decimal point if necessary, and continue the division until you've reached the desired precision.

Learn how to divide 754 by 1200 using the long division method with detailed steps. This guide walks you through performing decimal division, handling remainders, and achieving precision up to three decimal places. Suitable for Grades 5-7.

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