If the least count of a screw gauge is 0.001 cm and diameter of a wire measured by it is 0.236 cm, find the permissible percentage error in the measurement.

Explanation

To find the permissible percentage error in the measurement of the diameter of the wire using a screw gauge, we can follow these steps:

### Step 1: Identify the least count and the measured value
- The least count of the screw gauge (LC) is given as 0.001 cm.
- The measured diameter of the wire (D) is given as 0.236 cm.

### Step 2: Use the formula for percentage error
The formula for permissible percentage error is given by:

\[ \text{Percentage Error} = \left( \frac{\text{Least Count}}{\text{Measured Value}} \right) \times 100 \]

### Step 3: Substitute the values into the formula
Substituting the values we have:

\[ \text{Percentage Error} = \left( \frac{0.001 \text{ cm}}{0.236 \text{ cm}} \right) \times 100 \]

### Step 4: Calculate the fraction
Now, calculate the fraction:

\[ \frac{0.001}{0.236} \approx 0.00424 \]

### Step 5: Multiply by 100 to get the percentage
Now, multiply by 100 to convert it to a percentage:

\[ \text{Percentage Error} \approx 0.00424 \times 100 \approx 0.424\% \]

### Step 6: Round off the result
Rounding it off, we can say:

\[ \text{Permissible Percentage Error} \approx 0.42\% \]

### Final Answer:
The permissible percentage error in the measurement is approximately **0.42%**.

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