Question

The measured value of a quantity is \(98\) units, while the true value is \(100\) units. The percentage error is:

• A. \(1\%\)
• B. \(2\%\)
• C. \(3\%\)
• D. \(4\%\)

Hint:

Percentage error is always calculated by dividing absolute error by true value and then multiplying by \(100\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Error in a measurement is the difference between the experimental (measured) value and the actual (true) value.
Percentage error provides a standard way to express the accuracy of a measurement relative to the size of the quantity being measured. It tells us how far off the measurement is as a fraction of the true value.
Step 2: Key Formula or Approach:
The formula for percentage error is:
\[ \text{Percentage Error} = \frac{|\text{True Value} - \text{Measured Value}|}{\text{True Value}} \times 100% \]
Step 3: Detailed Explanation:
1. Identify the given parameters:
- True Value (\(T\)) = 100 units.
- Measured Value (\(M\)) = 98 units.
2. Calculate the absolute error:
\[ \text{Absolute Error} = |100 - 98| = 2 \text{ units} \]
3. Calculate the relative error:
\[ \text{Relative Error} = \frac{\text{Absolute Error}}{\text{True Value}} = \frac{2}{100} \]
4. Convert to percentage:
\[ \text{Percentage Error} = \frac{2}{100} \times 100% = 2% \]
Step 4: Final Answer:
The percentage error is exactly 2%.
This matches Option (B).