The unit of percentage error is

Options

A. Same as that of physical quantity
B. Different from that of physical quantity
C. Percentage error is unit less
D. Errors have got their own units which are different from that of physical quantity measured

Answer

To determine the unit of percentage error, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Percentage Error**:
The formula for percentage error is given by:
\[ \text{Percentage Error} = \frac{\text{Measured Value} - \text{Exact Value}}{\text{Exact Value}} \times 100 \]

2. **Substituting Values**:
Let's take an example where the measured value is 10.54 cm and the exact value is 10.5 cm. We can substitute these values into the formula:
\[ \text{Percentage Error} = \frac{10.54 \, \text{cm} - 10.5 \, \text{cm}}{10.5 \, \text{cm}} \times 100 \]

3. **Calculating the Difference**:
Calculate the difference between the measured and exact values:
\[ 10.54 \, \text{cm} - 10.5 \, \text{cm} = 0.04 \, \text{cm} \]

4. **Dividing by Exact Value**:
Now, divide the difference by the exact value:
\[ \frac{0.04 \, \text{cm}}{10.5 \, \text{cm}} = \frac{0.04}{10.5} \]

5. **Cancelling Units**:
Notice that the units (cm) in the numerator and denominator will cancel out:
\[ \frac{0.04}{10.5} \text{ (unitless)} \]

6. **Multiplying by 100**:
Finally, multiply by 100 to convert it into a percentage:
\[ \text{Percentage Error} = \left(\frac{0.04}{10.5}\right) \times 100 \]

7. **Conclusion on Units**:
Since the units cancel out in the calculation, the percentage error is a unitless quantity.

### Final Answer:
The unit of percentage error is **unitless**.