A student measured the diameter of a wire using a screw gauge with least count 0.001 cm and listed the measurements. The correct measurement is

Options

A. 5.3 cm
B. 5.32 cm
C. 5.320 cm
D. 5.3200 cm

Explanation

To determine the correct measurement of the diameter of the wire using a screw gauge with a least count of 0.001 cm, we need to analyze the options provided based on the precision indicated by the least count.

### Step-by-Step Solution:

1. **Identify the Least Count**: The least count of the screw gauge is given as 0.001 cm. This means that the smallest measurement that can be accurately read from the gauge is 0.001 cm.

2. **Understand the Implication of Least Count**: Since the least count is 0.001 cm, any measurement taken with this device should reflect three decimal places. This is because the least count indicates the precision of the measurement.

3. **Examine the Options**: We have four options to consider:
- Option 1: 5.3 cm
- Option 2: 5.32 cm
- Option 3: 5.320 cm
- Option 4: 5.3200 cm

4. **Evaluate Each Option**:
- **Option 1 (5.3 cm)**: This has only one digit after the decimal point. Since we need three digits after the decimal, this option is incorrect.
- **Option 2 (5.32 cm)**: This has two digits after the decimal point. Again, we need three digits, so this option is also incorrect.
- **Option 3 (5.320 cm)**: This has three digits after the decimal point, which matches the required precision based on the least count. This option is correct.
- **Option 4 (5.3200 cm)**: Although this option has four digits after the decimal, it is not necessary to have more than three digits for the measurement based on the least count. Therefore, this option is also incorrect.

5. **Conclusion**: The correct measurement of the diameter of the wire, based on the least count of the screw gauge, is **5.320 cm**.

### Final Answer:
The correct measurement is **5.320 cm**.