Round off the numbers $865250$ to four significant figures and compute Absolute Error, Relative Error, and Percentage error
My calculation is Absolute error-$50$, Relative error -$0.000057$, Percentage error - $0.0057%$.
But in my book, the answer is given an Absolute error - $50$, Relative error - $6.71 x 10^{-5}$, and Percentage Error - $6.71 x 10^{-3}$.
Could someone tell me what I am getting wrong?
Rounding off $x = 865250$ to four significant figures results in $x' = 865200$.
The error is given by $x - x' = 865250 - 865200 = 50$.
Absolute error
$$e_a = |x - x'| = 50$$
Relative error
$$e_r = \dfrac{e_a}{x} = \dfrac{50}{865250} = 0.0000577868 \approx 5.77 \times 10^{-5}$$
Percent error
$$e_p = 100 e_r = 100(0.0000577868) = 0.005778676683039585 \approx 5.77 \times 10^{-3}$$
I think there is a typo in the book.