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(c) Round off the following numbers to the number of decimal places indicated. \( \begin{array}{lll}\text { (1) } & 9,23584 \text { (3 decimal places) } & \text { (2) } 67,2436 \text { (2 decimal places) } \\ \text { (3) } 4,3768534 \text { (4 decimal places) } & \text { (4) } 17,247398(5 \text { decimal places) } \\ \text { (5) } 79,9999 \text { (3 decimal places) } & \text { (6) } 34,27846(4 \text { decimal places }) \\ \text { (7) } 5,555555 \text { (5 decimal places) } & \text { (8) } & 3 \pi \text { (3 decimal places) }\end{array} \)

Ask by Simpson Wyatt. in South Africa
Jan 27,2025

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Tutor-Verified Answer

Answer

Here are the numbers rounded to the specified decimal places: 1. **9.23584** → **9.236** 2. **67.2436** → **67.24** 3. **4.3768534** → **4.3769** 4. **17.247398** → **17.24740** 5. **79.9999** → **80.000** 6. **34.27846** → **34.2785** 7. **5.555555** → **5.55556** 8. **3π ≈ 9.42477796076938** → **9.425**

Solution

Certainly! Let's round each of the given numbers to the specified number of decimal places. ### (c) Rounded Numbers: 1. **9.23584** (3 decimal places) - **Rounded:** **9.236** - *Explanation:* The fourth decimal digit is 8 (≥5), so we round the third decimal up from 5 to 6. 2. **67.2436** (2 decimal places) - **Rounded:** **67.24** - *Explanation:* The third decimal digit is 3 (<5), so the second decimal remains unchanged. 3. **4.3768534** (4 decimal places) - **Rounded:** **4.3769** - *Explanation:* The fifth decimal digit is 5 (≥5), so we round the fourth decimal up from 8 to 9. 4. **17.247398** (5 decimal places) - **Rounded:** **17.24740** - *Explanation:* The sixth decimal digit is 8 (≥5), so we round the fifth decimal up from 9 to 10. This affects the fifth decimal place, resulting in an additional zero. 5. **79.9999** (3 decimal places) - **Rounded:** **80.000** - *Explanation:* Rounding up due to the fourth decimal digit being 9 leads to an increase in the whole number. 6. **34.27846** (4 decimal places) - **Rounded:** **34.2785** - *Explanation:* The fifth decimal digit is 6 (≥5), so we round the fourth decimal up from 4 to 5. 7. **5.555555** (5 decimal places) - **Rounded:** **5.55556** - *Explanation:* The sixth decimal digit is 5 (≥5), so we round the fifth decimal up from 5 to 6. 8. **3π** (3 decimal places) - **Calculation:** - \( \pi \approx 3.141592653589793 \) - \( 3\pi \approx 9.42477796076938 \) - **Rounded:** **9.425** - *Explanation:* The fourth decimal digit is 7 (≥5), so we round the third decimal up from 4 to 5. ### Summary Table: | **Problem** | **Original Number** | **Decimal Places** | **Rounded Number** | |-------------|---------------------|--------------------|--------------------| | (1) | 9.23584 | 3 | 9.236 | | (2) | 67.2436 | 2 | 67.24 | | (3) | 4.3768534 | 4 | 4.3769 | | (4) | 17.247398 | 5 | 17.24740 | | (5) | 79.9999 | 3 | 80.000 | | (6) | 34.27846 | 4 | 34.2785 | | (7) | 5.555555 | 5 | 5.55556 | | (8) | 3π ≈ 9.42477796076938| 3 | 9.425 | If you have any further questions or need additional explanations, feel free to ask!

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Extra Insights

To round off the numbers, follow these simple steps: first, identify the digit in the decimal place to which you want to round. If the next digit is 5 or greater, increase the last digit you want to keep by one, and if it's less than 5, just drop the remaining digits. 1) **9,23584 (3 decimal places)** becomes **9,236**. 2) **67,2436 (2 decimal places)** becomes **67,24**. 3) **4,3768534 (4 decimal places)** becomes **4,3769**. 4) **17,247398 (5 decimal places)** becomes **17,24740**. 5) **79,9999 (3 decimal places)** becomes **80,000**. 6) **34,27846 (4 decimal places)** becomes **34,2785**. 7) **5,555555 (5 decimal places)** becomes **5,55556**. 8) **3 π (3 decimal places)** approximates to **9,425** (as \( \pi \approx 3.14159 \)). Rounding is all about approximating numbers, making them easier to read or use in calculations, without losing significant value!

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