Answer
$\text{1) irrational number, }
\text{2) real number}
$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the definitions of the different classification of numbers.
$\bf{\text{Solution Details:}}$
Natural numbers are the numbers $\{1,2,3,...\}$.
Whole numbers are the numbers $\{0,1,2,3,...\}$.
Integers are the numbers $\{...,-3,-2,-1, 0,1,2,3,...\}.$
Rational numbers are numbers that can be expressed as the ratio between $2$ integers.
Irrational numbers are numbers that CANNOT be expressed as the ratio between $2$ integers.
Real numbers are the combined numbers in the set of rational and irrational numbers.
The given number, $
\dfrac{4\pi}{5}
,$ is a non-terminating and non-repeating number. Hence, it is classified as
\begin{array}{l}\require{cancel}
\text{1) irrational number, }
\text{2) real number}
.\end{array}
