-5/9 is rational, and its none of the other choices (integer, whole, irrational). So this value goes in the "rational" rectangle, and outside any other region.
The number [tex]-\sqrt{100}[/tex] turns into -10 after simplification. We see that this number is both rational and an integer. The best place for it is inside the "integer" circle. Note how this circle is entirely in the "rational" rectangle. We do not place it in the "whole number" circle because whole numbers are not negative.
The number [tex]\pi[/tex] is irrational since its decimal expansion goes on forever without any known pattern.
The number [tex]\sqrt{25}[/tex] simplifies to 5. This goes in the "whole number" circle.
Check out the diagram below.
