The diameter of a wire as measured by a screw gauge was found to be 1.002 cm, 1.000 cm, 1.006 cm .The absolute error in the second reading is

Options

A. 0.002 cm
B. 0.004 cm
C. 0.006 cm
D. 0.003 cm

Answer

To find the absolute error in the second reading of the diameter of the wire measured by the screw gauge, we will follow these steps:

### Step 1: Identify the Measurements
The three measurements of the diameter of the wire are:
- First reading: 1.002 cm
- Second reading: 1.000 cm
- Third reading: 1.006 cm

### Step 2: Calculate the Mean Value
To find the mean value of the measurements, we will sum the three readings and divide by the number of readings (which is 3).

\[ \text{Mean Value} = \frac{1.002 + 1.000 + 1.006}{3} \]

Calculating the sum:
\[ 1.002 + 1.000 + 1.006 = 3.008 \]

Now, divide by 3:
\[ \text{Mean Value} = \frac{3.008}{3} = 1.0026667 \text{ cm} \]

### Step 3: Round the Mean Value
We need to round the mean value to three decimal places. The last digit is 6, which is greater than 5, so we round up the last digit:

\[ \text{Rounded Mean Value} = 1.003 \text{ cm} \]

### Step 4: Calculate the Absolute Error for the Second Reading
The absolute error in the second reading is calculated by taking the difference between the mean value and the second reading.

\[ \text{Absolute Error} = \text{Mean Value} - \text{Second Reading} \]
\[ \text{Absolute Error} = 1.003 \text{ cm} - 1.000 \text{ cm} = 0.003 \text{ cm} \]

### Conclusion
The absolute error in the second reading is **0.003 cm**.

---