Question

When the original value of N in urea is 46% and the estimated value is 5 %,then the relative error is _________ %.

• A. 0.5
• B. 1.087
• C. 0.005
• D. 0.1068

Hint:

Always divide the absolute error by the true (original) value rather than the experimental estimated value to calculate the correct relative error.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In analytical measurements, error analysis evaluates the accuracy of an experimental value.
- Absolute Error is the absolute difference between the experimental (estimated) value and the true (original) value.
- Relative Error is the absolute error divided by the true value, often expressed as a percentage.

Step 2: Key Formula or Approach:
The formula for relative error percent is:
\[ \text{Relative Error (\%)} = \frac{|\text{Estimated Value} - \text{True Value}|}{\text{True Value}} \times 100 \]

Step 3: Detailed Explanation:
Let us extract the values from the problem statement:
- True (original) value of N in urea = $46\%$
- Estimated (experimental) value of N in urea = $5\%$
First, calculate the absolute error:
\[ \text{Absolute Error} = |5 - 46| = 0.5\% \]
Next, calculate the relative error percent by dividing the absolute error by the true value ($46$):
\[ \text{Relative Error (\%)} = \frac{0.5}{46} \times 100 \]
\[ \text{Relative Error (\%)} = 0.0108695 \times 100 \]
\[ \text{Relative Error (\%)} \approx 1.08695\% \]
Rounding to three decimal places, we get $1.087\%$.
Let us review the options:
- Option (A) is the absolute error ($0.5$).
- Option (B) is the correct calculated relative error ($1.087\%$).
- Options (C) and (D) are incorrect.

Step 4: Final Answer:
The relative error is $1.087\%$, corresponding to option (B).