Question

The measured length of a rod is (20.0 $\pm$ 0.2) cm. The percentage error in the measurement is:

• A. 0.5%
• B. 1%
• C. 2%
• D. 5%

Hint:

To calculate percentage error quickly:
Shift the decimal point of both the absolute error and the measured value to make the math simpler.
Here, $\frac{0.2}{20} \times 100 = \frac{2}{200} \times 100 = \frac{2}{2} = 1\%$.
Always double check that both values have the same unit of measurement.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This question is from the topic "Units and Measurements," specifically focusing on Error Analysis.
We are given the measurement of a rod along with its absolute error, and we need to calculate the percentage error.

Step 2: Key Formula or Approach:
The percentage error is defined as the relative error multiplied by 100:
\[ \text{Percentage Error} = \frac{\text{Absolute Error } (\Delta L)}{\text{Measured Value } (L)} \times 100\% \]

Step 3: Detailed Explanation:

• We are given the measurement as:
\[ \text{Length} = (20.0 \pm 0.2)\text{ cm} \]
This indicates:
Measured value of length ($L$) = $20.0\text{ cm}$
Absolute error in length ($\Delta L$) = $0.2\text{ cm}$

• Substitute these values into the percentage error formula:
\[ \text{Percentage Error} = \frac{0.2\text{ cm}}{20.0\text{ cm}} \times 100\% \]

• Simplify the fraction:
\[ \frac{0.2}{20.0} = \frac{2}{200} = 0.01 \]

• Multiply by 100 to get the percentage value:
\[ \text{Percentage Error} = 0.01 \times 100\% = 1\% \]

• Percentage error indicates the relative precision of a measurement; a lower percentage error means higher precision and reliability of the measurement.



Step 4: Final Answer:
The percentage error in the measurement is $1\%$, which corresponds to option (B).