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 find the percentage error in the measurement of the thickness of a pencil using a screw gauge, we can follow these steps:

### Step 1: Identify the given values
- Thickness of the pencil (measured value, x) = 0.802 cm
- Least count of the screw gauge (which is the error, Δx) = 0.001 cm

### Step 2: Understand the formula for percentage error
The formula for percentage error is given by:
\[ \text{Percentage Error} = \left( \frac{\Delta x}{x} \right) \times 100 \]
where Δx is the error in measurement and x is the measured value.

### Step 3: Substitute the values into the formula
Now, substituting the values we have:
\[ \text{Percentage Error} = \left( \frac{0.001 \, \text{cm}}{0.802 \, \text{cm}} \right) \times 100 \]

### Step 4: Calculate the percentage error
Now, perform the division:
\[ \frac{0.001}{0.802} \approx 0.001248 \]
Then multiply by 100 to get the percentage:
\[ \text{Percentage Error} \approx 0.001248 \times 100 \approx 0.1248 \]

### Step 5: Round off the result
Rounding off to three decimal places, we find:
\[ \text{Percentage Error} \approx 0.125\% \]

### Final Answer
Thus, the percentage error in the measurement of the thickness of the pencil is approximately **0.125%**.

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