Thickness of a pencil measured by using a screw gauge (least count.001 cm) comes out to be 0.802 cm .The percentage error in the measurement is

Options

A. `0.125%`
B. `2.43%`
C. `4.12%`
D. `2.14%`

Answer

To calculate the percentage error in the measurement of the thickness of the pencil, we can follow these steps:

### Step 1: Identify the measured value and the least count
- Measured value (thickness of the pencil) = 0.802 cm
- Least count of the screw gauge = 0.001 cm

### Step 2: Calculate the absolute error
The absolute error is equal to the least count of the measuring instrument. Therefore:
- Absolute error = Least count = 0.001 cm

### Step 3: Calculate the percentage error
The percentage error can be calculated using the formula:
\[ \text{Percentage Error} = \left( \frac{\text{Absolute Error}}{\text{Measured Value}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Error} = \left( \frac{0.001 \, \text{cm}}{0.802 \, \text{cm}} \right) \times 100 \]

### Step 4: Perform the calculation
Calculating the fraction:
\[ \frac{0.001}{0.802} \approx 0.001246 \]
Now, multiply by 100 to get the percentage:
\[ \text{Percentage Error} \approx 0.001246 \times 100 \approx 0.1246\% \]

### Final Result
The percentage error in the measurement is approximately **0.125%** (rounded to three decimal places).

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