A cup holds 200ml to the nearest ml, and a large container holds 86 litres to the nearest litre. What is the largest possible number of cups of water needed to fill the container? What is the smallest possible number of cups?

We need to calculate both the **largest** and **smallest possible number of cups** needed to fill the large container, taking into account rounding errors for both the cup and the container.

### Step-by-step solution:

1. **Cup Volume (200 ml) to nearest ml:**
   - **Minimum volume**: \(199.5 \, \text{ml}\)
   - **Maximum volume**: \(200.5 \, \text{ml}\)

2. **Container Volume (86 litres) to nearest litre:**
   - **Minimum volume**: \(85.5 \, \text{litres}\)
   - **Maximum volume**: \(86.5 \, \text{litres}\)

   Note: 1 litre = 1000 ml, so:
   - **85.5 litres** = \(85.5 \times 1000 = 85,500 \, \text{ml}\)
   - **86.5 litres** = \(86.5 \times 1000 = 86,500 \, \text{ml}\)

---

### Largest Possible Number of Cups:
To get the largest number of cups, we divide the largest possible container volume by the smallest possible cup volume.

\[
\frac{86,500 \, \text{ml}}{199.5 \, \text{ml}} \approx 433.58
\]

Since only full cups count, we round up:
\[
434 \, \text{cups}
\]

---

### Smallest Possible Number of Cups:
To get the smallest number of cups, we divide the smallest possible container volume by the largest possible cup volume.

\[
\frac{85,500 \, \text{ml}}{200.5 \, \text{ml}} \approx 426.68
\]

Rounding up (since even partial cups are not allowed), we get:
\[
427 \, \text{cups}
\]

---

### Final Answer:
- **Largest possible number of cups**: 434 cups  
- **Smallest possible number of cups**: 427 cups

---

Would you like further details or have any questions?  

Here are 5 related questions:  
1. How do rounding errors affect real-world measurements?  
2. What is the difference between significant figures and decimal places?  
3. How do you convert between different units of volume?  
4. Why do we round up when calculating the number of cups?  
5. How would the answer change if the container held 87 litres instead?

**Tip:** Always account for rounding errors when dealing with real-world measurements, especially for precise calculations!

Explore how to estimate the largest and smallest possible number of 200ml cups needed to fill an 86-litre container. This problem uses rounding, division, and unit conversions, providing a clear, step-by-step guide for Grades 6-8 students.

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