The length of a rug was measured as 2.17m. If the actual length of the rug is 2.075m, then which of the following is not a possible limiting absolute error.

To solve this problem, we need to first understand the concept of limiting absolute error and then determine which of the provided options is not a possible limiting absolute error.

### Concept:
The **absolute error** is the difference between the measured value and the actual value of the length. It is given by:
\[
\text{Absolute Error} = |\text{Measured Value} - \text{Actual Value}|
\]

The **limiting absolute error** refers to the maximum possible absolute error based on the precision of the measurement.

### Given:
- Measured length of the rug = \( 2.17 \, \text{m} \)
- Actual length of the rug = \( 2.075 \, \text{m} \)

### Step 1: Calculate the Absolute Error
The absolute error between the measured and actual length is:
\[
\text{Absolute Error} = |2.17 - 2.075| = 0.095 \, \text{m}
\]

### Step 2: Analyze the Limiting Absolute Error
The limiting absolute error depends on the precision of the measurement tool. Since the measured value was given as \( 2.17 \, \text{m} \), the precision of the measurement tool is up to two decimal places. This means the **least count** or **smallest division** that the measuring tool can distinguish is \( 0.01 \, \text{m} \).

Thus, the limiting absolute error should be in the range of possible values that a measurement tool with a precision of \( 0.01 \, \text{m} \) can generate. Common values for limiting absolute error would typically include values around the least count, like \( 0.01 \, \text{m} \), \( 0.02 \, \text{m} \), etc.

### Conclusion:
Now, if you provide me with a list of possible limiting absolute error options, I can determine which one is **not** feasible given the context of the precision and measurement error. Could you share the options?

---

Do you have any questions or want to provide the options?  
Here are 5 relevant follow-up questions:
1. What does relative error mean in a measurement?
2. How does the precision of an instrument impact the limiting error?
3. Can the limiting absolute error be smaller than the smallest division of a measurement tool?
4. What are the consequences of overestimating the absolute error?
5. How can you reduce measurement errors in practical experiments?

**Tip:** Always double-check the least count of your measuring instrument to determine the limiting absolute error effectively.

Explore how to calculate and determine the limiting absolute error in a measurement problem involving the length of a rug. Given the measured length of 2.17m and the actual length of 2.075m, learn how to assess which possible limiting absolute error values are valid. Suitable for students in Grades 9-11.

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