The breadth of a thin rectangular sheet is measured as 10.1 cm. The approximate error in the measurement is

Options

A. `pm1%`
B. `pm0.5%`
C. `pm0.1%`
D. `pm5%`

Answer

To solve the problem of determining the approximate error in the measurement of the breadth of a thin rectangular sheet measured as 10.1 cm, we can follow these steps:

### Step 1: Identify the measured value and its uncertainty
The measured breadth of the sheet is given as 10.1 cm. The approximate error (or uncertainty) in this measurement is typically taken as half of the smallest division of the measuring instrument. In this case, we can assume the uncertainty to be ±0.1 cm.

### Step 2: Write down the formula for percentage error
The formula for calculating the percentage error is given by:

\[ \text{Percentage Error} = \left( \frac{\Delta B}{B} \right) \times 100 \]

Where:
- \(\Delta B\) is the uncertainty in the measurement (±0.1 cm)
- \(B\) is the measured value (10.1 cm)

### Step 3: Substitute the values into the formula
Now, substituting the values into the formula:

\[ \text{Percentage Error} = \left( \frac{0.1 \text{ cm}}{10.1 \text{ cm}} \right) \times 100 \]

### Step 4: Calculate the percentage error
Calculating the above expression:

1. Divide 0.1 by 10.1:
\[ \frac{0.1}{10.1} \approx 0.00990099 \]

2. Multiply by 100 to convert it into a percentage:
\[ 0.00990099 \times 100 \approx 0.990099 \approx 1\% \]

### Step 5: State the final result
Thus, the approximate error in the measurement of the breadth of the thin rectangular sheet is ±1%.