The length of a rod is measured by four different instruments and the measurements are reported as
A. 500.0 mm , B. 50.0 cm , C.0.500 m , D. `5.0xx10^(-4)` km
We can conclude that

Options

A. A is most accurate measurement
B. C is most accurate measurement
C. A, C and B are equally accurate measurements
D. The accuracy of all the measurements is the same

Answer

To solve the problem, we need to analyze the measurements provided and determine which instrument gives the most precise measurement based on the number of significant figures.

### Step-by-step Solution:

1. **Identify the Measurements and Their Units**:
- A: 500.0 mm
- B: 50.0 cm
- C: 0.500 m
- D: \(5.0 \times 10^{-4}\) km

2. **Convert All Measurements to the Same Unit** (optional for understanding, but not necessary for significant figures):
- A: 500.0 mm = 0.5000 m (since 1 mm = 0.001 m)
- B: 50.0 cm = 0.5000 m (since 1 cm = 0.01 m)
- C: 0.500 m (already in meters)
- D: \(5.0 \times 10^{-4}\) km = 0.0005 m (since 1 km = 1000 m)

3. **Determine the Number of Significant Figures**:
- A: 500.0 mm has **4 significant figures** (the decimal point indicates that the zeros are significant).
- B: 50.0 cm has **3 significant figures** (the trailing zero after the decimal is significant).
- C: 0.500 m has **3 significant figures** (the leading zero is not significant, but the trailing zeros after the decimal are).
- D: \(5.0 \times 10^{-4}\) km has **2 significant figures** (the trailing zero after the decimal is significant).

4. **Compare the Significant Figures**:
- A has the highest number of significant figures (4), followed by B and C (3 each), and D has the least (2).

5. **Conclusion**:
- Since A has the maximum number of significant figures, we can conclude that the measurement from instrument A (500.0 mm) is the most accurate.

### Final Answer:
The measurement from instrument A (500.0 mm) is the most accurate due to having the highest number of significant figures (4).

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