Express the range in which the length and width of a rectangular playing field lie, considering that the dimensions were measured to the nearest meter, with the length recorded as 350 meters and the width recorded as 200 meters.

To express the range in which the length and width of the rectangular playing field lie, considering that the measurements were taken to the nearest meter, we can use the concept of tolerance or rounding.

### Length:
- The recorded length is 350 meters. 
- Since the length was rounded to the nearest meter, the actual length lies within 0.5 meters of this value, i.e., from \(349.5 \, \text{m}\) to \(350.5 \, \text{m}\).

Thus, the length range is:
\[
349.5 \, \text{m} \leq L \leq 350.5 \, \text{m}
\]

### Width:
- The recorded width is 200 meters.
- Similarly, the actual width lies within 0.5 meters of this value, i.e., from \(199.5 \, \text{m}\) to \(200.5 \, \text{m}\).

Thus, the width range is:
\[
199.5 \, \text{m} \leq W \leq 200.5 \, \text{m}
\]

### Conclusion:
The ranges for the dimensions are:
- Length: \(349.5 \, \text{m} \leq L \leq 350.5 \, \text{m}\)
- Width: \(199.5 \, \text{m} \leq W \leq 200.5 \, \text{m}\)

Would you like further details on this topic or have any questions?

Here are 5 related questions:
1. How would the perimeter of the field vary within these ranges?
2. How would you calculate the area using these dimensional ranges?
3. What is the maximum possible perimeter based on the ranges?
4. How does tolerance affect measurement accuracy in general?
5. How would these tolerances affect the design of a fence around the field?

**Tip:** When dealing with measurements rounded to the nearest unit, always account for a possible deviation of half a unit on either side.

Understand how to calculate the range of dimensions for a rectangular field when length and width are measured to the nearest meter. Learn about the tolerance in measurement, and how rounding affects the final results. The length is recorded as 350 meters and the width as 200 meters, with ranges calculated using inequalities. Suitable for Grades 6-8.

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