Question:
The measured value of a quantity is 98 units, while the true value is 100 units. The percentage error is:
The measured value of a quantity is 98 units, while the true value is 100 units. The percentage error is:
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When the true value is exactly $100$ units, the absolute error is directly equal to the percentage error. You can compute this instantly in your head without standard formulas!
Updated On: Jun 3, 2026
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
The question asks us to calculate the percentage error in a measurement where the true (actual) value is $100$ units and the experimentally measured value is $98$ units.
Step 2: Key Formula or Approach:
The formula for percentage error is: \[ \text{Percentage Error} = \frac{|\text{True Value} - \text{Measured Value}|}{\text{True Value}} \times 100\% \] This can be written as: \[ \text{Percentage Error} = \frac{\Delta x}{T} \times 100\% \] where $\Delta x$ is the absolute error and $T$ is the true value.
Step 3: Detailed Explanation:
• Identify the given parameters:
True Value ($T$) = $100$ units
Measured Value ($M$) = $98$ units
• Compute the absolute error ($\Delta x$):
\[ \Delta x = | 100 - 98 | = 2 \text{ units} \]
• Apply the percentage error formula:
\[ \text{Percentage Error} = \frac{2}{100} \times 100\% = 2\% \]
• This shows that the experimental measurement has a deviation of exactly $2\%$ from the true value.
Step 4: Final Answer:
The percentage error in the measurement is $2\%$.
The question asks us to calculate the percentage error in a measurement where the true (actual) value is $100$ units and the experimentally measured value is $98$ units.
Step 2: Key Formula or Approach:
The formula for percentage error is: \[ \text{Percentage Error} = \frac{|\text{True Value} - \text{Measured Value}|}{\text{True Value}} \times 100\% \] This can be written as: \[ \text{Percentage Error} = \frac{\Delta x}{T} \times 100\% \] where $\Delta x$ is the absolute error and $T$ is the true value.
Step 3: Detailed Explanation:
• Identify the given parameters:
True Value ($T$) = $100$ units
Measured Value ($M$) = $98$ units
• Compute the absolute error ($\Delta x$):
\[ \Delta x = | 100 - 98 | = 2 \text{ units} \]
• Apply the percentage error formula:
\[ \text{Percentage Error} = \frac{2}{100} \times 100\% = 2\% \]
• This shows that the experimental measurement has a deviation of exactly $2\%$ from the true value.
Step 4: Final Answer:
The percentage error in the measurement is $2\%$.
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