A program evaluates at on a calculator that rounds every result to eight significant…
PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Numerical and computational mathematics · Numerical and computational mathematics
Mathematical Methods for Physics, Ch Floating-point arithmetic, conditioning and numerical stability
Problem
A program evaluates f(x)=x+1−x at x=108 on a calculator that rounds every result to eight significant figures.
((a)) Say which operation is at risk, predict how many of the eight figures the direct evaluation keeps, and carry it out.
((b)) Rewrite f(x) so that no two nearly equal numbers are subtracted, and evaluate the rewrite on the same calculator.
((c)) Find the true value from the first two terms of the binomial series for x[(1+1/x)1/2−1], and count the correct figures in each answer.