## Task 2 - 120912

During a GST exercise, Andreas and Frank estimated the length of a distance. If Andreas had estimated $10 \%$ less, he would have hit the exact length. If Frank's estimate had been $10 \%$ higher, he would have hit the exact length of the distance.

In which of the two estimates is the absolute value of the absolute error smaller?
The exact length of the distance $S$ is, according to Andreas's estimate $A$, 10% lower than his value; thus at $\frac{9}{10} A=S$. Frank's estimate $F$ must be increased by 10% to obtain the exact value $S$; thus $\frac{11}{10} F=S$. Andreas's value is therefore $A=\frac{10}{9} S$ and the magnitude of the absolute error $A=\left|\frac{10}{9} S-S\right|=\frac{1}{9} S$. Frank's value is $F=\frac{10}{11} S$ and the magnitude of the absolute error

$F=\left|\frac{10}{11} S-S\right|=\frac{1}{11} S$. Frank's estimated value has a smaller magnitude of absolute error than Andreas's estimated value $\left(\frac{1}{11} S<\frac{1}{9} S\right)$.