1. **Problem statement:** (A) Considering an exact value of variable $a = \sqrt{2}$ and its approximate $\bar{a} = 1.414$, describe the basic concepts of errors. 2. **Formula and explanation:** The **absolute error** is defined as the difference between the exact value and the approximate value: $$\text{Absolute error} = |a - \bar{a}|$$ The **relative error** is the absolute error divided by the exact value: $$\text{Relative error} = \frac{|a - \bar{a}|}{|a|}$$ 3. **Calculation:** Given $a = \sqrt{2} \approx 1.414213562$ and $\bar{a} = 1.414$, $$\text{Absolute error} = |1.414213562 - 1.414| = 0.000213562$$ $$\text{Relative error} = \frac{0.000213562}{1.414213562} \approx 0.000151$$ 4. **Interpretation:** Absolute error tells us how far the approximation is from the exact value in units. Relative error tells us how significant this error is compared to the size of the exact value. 5. **Summary:** Errors measure the difference between exact and approximate values, helping us understand the accuracy of numerical results.