Question

When the original value of N in urea is 46%, the estimated value is 45.5 %, then the absolute error is -----

• A. 0.5
• B. 1.06
• C. 0.05
• D. 0.106

Hint:

Always distinguish between absolute error and relative error.
Absolute error is simply the positive difference: \( |\text{True} - \text{Measured}| \).
Relative error is the absolute error divided by the true value, which would be \( \frac{0.5}{46} \approx 1.087\% \).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Error analysis is a fundamental aspect of analytical chemistry and soil testing.
When measuring chemical concentrations, such as nitrogen (N) in fertilizers, the difference between the true value and the measured value must be quantified.
Absolute error is a direct measure of this difference and has the same units as the measured quantity.
Key Formula or Approach:
The absolute error (\( e_a \)) is calculated using the following formula:
\[ e_a = |x_{\text{true}} - x_{\text{measured}}| \]
where:
- \( x_{\text{true}} \) is the true or original value of the analyte.
- \( x_{\text{measured}} \) is the estimated or measured value.

Step 2: Detailed Explanation:
In this problem, the true value of nitrogen (N) in pure urea is:
\[ x_{\text{true}} = 46\% \]
The estimated or measured value of N is:
\[ x_{\text{measured}} = 45.5\% \]
Substituting these values into the absolute error formula:
\[ e_a = |46\% - 45.5\%| \]
\[ e_a = 0.5\% \]
Thus, the absolute difference between the true value and the estimated value is 0.5.
This absolute error represents the magnitude of deviation without considering the direction of the error or the proportion relative to the true value.

Step 3: Final Answer:
The absolute error of the estimation is 0.5.