Pick up the most acurate and most precise measurements out of the following

Options

A. 50.00m is the most accurate measurement
B. 5.00m is the most accurate measurement
C. 5.00 cm is the most precise measurement
D. 5.00 mm is the most precise measurement

Answer

To determine the most accurate and most precise measurements from the given options, we need to understand the concepts of accuracy and precision.

### Definitions:
1. **Accuracy**: Refers to how close a measured value is to the actual (true) value. It is often assessed by calculating the fractional or relative error.
2. **Precision**: Refers to how close multiple measurements are to each other. It is often indicated by the number of decimal places in the measurement.

### Steps to Solve the Question:

1. **Identify the Measurements**:
- Let's assume the options provided are:
- Option A: 50.00 m
- Option B: 5.00 m
- Option C: 50.0 mm
- Option D: 5.00 mm

2. **Calculate the Possible Errors**:
- For a measurement on a meter scale, the least count (possible error) is typically 0.01 m.
- For a measurement on a millimeter scale, the least count (possible error) is typically 0.01 mm.

3. **Calculate the Relative Errors**:
- For **Option A (50.00 m)**:
- Possible error = 0.01 m
- Relative error = (0.01 m) / (50.00 m) = 0.0002 or 2 x 10^-4
- For **Option B (5.00 m)**:
- Possible error = 0.01 m
- Relative error = (0.01 m) / (5.00 m) = 0.002 or 2 x 10^-3
- For **Option C (50.0 mm)**:
- Possible error = 0.01 mm = 0.00001 m
- Relative error = (0.01 mm) / (50.0 mm) = 0.0002 or 2 x 10^-4
- For **Option D (5.00 mm)**:
- Possible error = 0.01 mm = 0.00001 m
- Relative error = (0.01 mm) / (5.00 mm) = 0.002 or 2 x 10^-3

4. **Determine the Most Accurate Measurement**:
- The measurement with the least relative error is the most accurate.
- Comparing the relative errors:
- Option A: 2 x 10^-4
- Option B: 2 x 10^-3
- Option C: 2 x 10^-4
- Option D: 2 x 10^-3
- Options A and C have the least relative error (2 x 10^-4), making them the most accurate.

5. **Determine the Most Precise Measurement**:
- The measurement with the most decimal places is the most precise.
- Comparing the decimal places:
- Option A: 50.00 m (4 decimal places)
- Option B: 5.00 m (3 decimal places)
- Option C: 50.0 mm (3 decimal places)
- Option D: 5.00 mm (3 decimal places)
- Option A has the most decimal places, making it the most precise.

### Conclusion:
- **Most Accurate Measurement**: Options A (50.00 m) and C (50.0 mm) are equally accurate.
- **Most Precise Measurement**: Option A (50.00 m) is the most precise.