#### Answer

a.) 100
b.) 0, 100, -8
c.) -1.5, 0, $\frac{5}{2}$, 2.71, 3.1$\overline{4}$, 100, -8
d.) $\sqrt 7$, -$\pi$

#### Work Step by Step

Natural numbers are integers and integers are rational numbers.
The numbers included (-1.5, 0, $\frac{5}{2}$, 2.71, 3.1$\overline{4}$, 100, -8, $\sqrt 7$, -$\pi$ ) can be categorized in the sections
a.) Natural numbers - whole Positive integers greater than zero (Ex. 1, 2, 3, 4...).
This only includes 100.
b.) Integers - every whole number (ex. -1, 0, 1, 2...)
This includes 0, 100, and -8
c.) Rational Numbers- any number that is whole or fractional (Ex. $\frac{2}{5}$ , 7).
This includes -1.5, 0, $\frac{5}{2}$, 2.71, 3.1$\overline{4}$, 100, and -8
d.)Irrational Numbers- Numbers that cannot be expressed as a ratio of integers (Ex. $\sqrt 2$, $\pi$). This is separate for the rational number section.
This only includes $\sqrt 7$ and -$\pi$