The error of an approximation can be described as the difference between the actual value and the estimated value. In this case, if the error bound is negative, it means that the approximation is an overestimate. This implies that the calculated value is higher than the actual value.
To determine the absolute value of the error bound, you would need to consider the magnitude of the error without regard to its sign. This can be calculated by taking the absolute value of the error bound, which would provide a positive value representing the distance between the actual value and the approximation.
If you are asked to round the absolute value of the error bound to five decimal places, you would simply retain the first five digits after the decimal point and round the final digit as necessary. This ensures a precise and standardized representation of the error magnitude.
In summary, when dealing with error bounds and approximations, understanding whether the error is positive or negative helps in determining whether the approximation is an overestimate or an underestimate. Calculating the absolute value of the error bound provides a clear measure of the discrepancy between the actual and estimated values, ensuring an accurate assessment of the approximation quality.
