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8. \( 7 6 0 \longdiv { 1 8 0 0 0 0 } \)

Ask by Vega John. in South Africa
Jan 27,2025

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Answer

The division of 180,000 by 760 is approximately 236.8421.

Solution

Certainly! Let's perform the long division of **180,000** divided by **760** step by step. ### Long Division: 180,000 ÷ 760 ``` 236.8421... ____________________ 760 ) 180000.000000 1520 ---- 2800 2280 ---- 5200 4560 ---- 6400 6080 ---- 3200 3040 ---- 1600 1520 ---- 800 760 ---- 400 ``` ### Step-by-Step Explanation 1. **Initial Setup**: - **Divisor**: 760 - **Dividend**: 180,000 - We'll add decimal places to the dividend to continue the division beyond the whole number. 2. **First Division**: - Determine how many times 760 fits into the first part of the dividend. - **760 × 2 = 1520** fits into 1800. - **Subtract**: 1800 - 1520 = **280** - **Bring down** the next digit (0) to make it **2800**. 3. **Second Division**: - **760 × 3 = 2280** fits into 2800. - **Subtract**: 2800 - 2280 = **520** - **Bring down** the next digit (0) to make it **5200**. 4. **Third Division**: - **760 × 6 = 4560** fits into 5200. - **Subtract**: 5200 - 4560 = **640** - **Bring down** the next digit (0) to make it **6400**. 5. **Fourth Division**: - **760 × 8 = 6080** fits into 6400. - **Subtract**: 6400 - 6080 = **320** - **Bring down** the next digit (0) to make it **3200**. 6. **Fifth Division**: - **760 × 4 = 3040** fits into 3200. - **Subtract**: 3200 - 3040 = **160** - **Bring down** the next digit (0) to make it **1600**. 7. **Sixth Division**: - **760 × 2 = 1520** fits into 1600. - **Subtract**: 1600 - 1520 = **80** - **Bring down** the next digit (0) to make it **800**. 8. **Seventh Division**: - **760 × 1 = 760** fits into 800. - **Subtract**: 800 - 760 = **40** - **Bring down** the next digit (0) to make it **400**. 9. **Continuing the Process**: - You can continue adding zeros to the dividend to get more decimal places as needed. - The division will continue with the remainder getting smaller. ### Final Result The division of **180,000 ÷ 760** results in: \[ \frac{180,000}{760} = 236.842105\ldots \] So, **180,000 ÷ 760 ≈ 236.8421** ### Summary - **Whole Number Part**: 236 - **Decimal Part**: Approximately 0.8421 - **Final Answer**: **236.8421**

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The Deep Dive

Did you know that long division has been around for centuries? It dates back to ancient civilizations, including the Babylonians and Greeks, who used various methods to divide numbers, often for trade and land distribution. The process you're using today, with the neat layout and step-by-step approach, became more standardized in the 15th century and is still taught in classrooms around the world! Now, let’s dive into some real-world applications! Long division is not just a school exercise; it's crucial in fields like computer science, where operations need to be broken down into manageable parts. For example, algorithms for tasks like data encryption or error detections often require precise division to operate efficiently. So, mastering long division can set you up for success in advanced problem-solving scenarios!

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