A measurement gives one second for the period of the same star decide which of the measurement will be most accurate and which will be most precise 0.9 seconds plus -0.20% B between 0.990 seconds and one second see 1.02 seconds 1.010 seconds plus -0.001 seconds

To determine which measurement is the most accurate and which is the most precise, let's analyze each option in the context of the given period of the star, which is 1 second.

### Given Measurements:
1. **A: 0.9 seconds ± 0.20%**
   - The uncertainty is \(0.20\%\) of 0.9 seconds.
   - \(0.20\%\) of 0.9 seconds = \(0.002 \times 0.9 = 0.0018\) seconds.
   - Therefore, the measurement is \(0.9 \pm 0.0018\) seconds, so it could range from \(0.8982\) seconds to \(0.9018\) seconds.

2. **B: Between 0.990 seconds and 1 second**
   - This measurement is given as a range.
   - The midpoint is \( \frac{0.990 + 1.000}{2} = 0.995 \) seconds.
   - The range is \( \pm 0.005 \) seconds.

3. **C: 1.02 seconds**
   - This is a single value with no indication of uncertainty.

4. **D: 1.010 seconds ± 0.001 seconds**
   - This measurement has a specified uncertainty.
   - Therefore, it ranges from \(1.009\) seconds to \(1.011\) seconds.

### Evaluating Accuracy:
- The most accurate measurement is the one closest to 1 second.
  - **A**: The midpoint is 0.9 seconds, which is \( |0.9 - 1.0| = 0.1 \) seconds away from 1 second.
  - **B**: The midpoint is 0.995 seconds, which is \( |0.995 - 1.0| = 0.005 \) seconds away from 1 second.
  - **C**: 1.02 seconds is \( |1.02 - 1.0| = 0.02 \) seconds away from 1 second.
  - **D**: 1.010 seconds is \( |1.010 - 1.0| = 0.01 \) seconds away from 1 second.

  Therefore, **B** (between 0.990 seconds and 1 second) is the most accurate measurement because its midpoint (0.995 seconds) is closest to 1 second.

### Evaluating Precision:
- The most precise measurement has the smallest uncertainty or range.
  - **A**: The uncertainty is 0.0018 seconds.
  - **B**: The range is 0.005 seconds (0.990 to 1.000 seconds).
  - **C**: No precision provided (no uncertainty).
  - **D**: The uncertainty is 0.001 seconds.

  Therefore, **D** (1.010 seconds ± 0.001 seconds) is the most precise measurement due to its smallest uncertainty.

### Summary:
- **Most Accurate:** Measurement **B** (between 0.990 seconds and 1 second)
- **Most Precise:** Measurement **D** (1.010 seconds ± 0.001 seconds)

Would you like more details or have any questions?

Here are five questions that expand on this topic:
1. What are some real-life scenarios where both high accuracy and high precision are crucial?
2. How does the size of the uncertainty affect the precision of a measurement?
3. Can a measurement with a larger uncertainty ever be considered more accurate? Why or why not?
4. What are some techniques used to improve both accuracy and precision in time measurements?
5. How do repeated measurements help in determining the precision of a measurement?

**Tip:** When reporting measurements, always include the uncertainty to give a clear indication of the precision and reliability of the data.

Explore how to determine accuracy and precision in time measurements using examples of measurements around 1 second. Analyze different measurement methods including their uncertainties and ranges. Learn about the importance of accuracy and precision in scientific measurements.

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