## Task 5 - 080835

Fritz is supposed to multiply a three-digit natural number $z$ by itself. By mistake, he writes the first factor as a number 5 less. When this is pointed out to him, he says: "I'll just take the second factor as a number 5 greater, then the result will be correct."

a) Is this statement true?

b) Assuming it is false, within what limits does the absolute error move if $z$ runs through all three-digit numbers?
a) Fritz should calculate: $z \cdot z=z^{2}$. He calculated: $(z-5)(z+5)=z^{2}-25$. His way is therefore wrong.

b) The absolute error is in every case: -25.

It is thus not different depending on the number $z$, but constant.