One of the most serious errors in computer calculations occurs when two nearly equal numbers are subtracted. Consider A = 0.22288 and B = 0.22211. The computer truncates all values to four decimal digits. Thus A′ = 0.2228 and B′ = 0.2221.
a. What are the relative errors for A′ and B′?
b. What is the relative error for C′ = A′ - B′?