Name the sets of numbers to which each number belongs.

$-4.\overline{2}$

A number that can be stated as an infinite decimal expansion.

Real numbers are numbers that include both rational and irrational numbers.

All numbers that is whole numbers, integers, natural number, rational and irrational numbers are real numbers.

Here, the number is $-4.\overline{2}$.

Natural numbers are $\left\{1,2,3,...\right\}$ is not a natural number.

Whole numbers are $\left\{0,1,2,3,...\right\}$. Then $-4.\overline{2}$ is not a whole number.

Integers are $\left\{...,-3,-2,-1,0,1,2,3,...\right\}$. Then $-4.\overline{2}$ is not an integer.

Since $-4.\overline{2}$ can be expressed as $\frac{m}{n}$ form that is:

Let $x=-4.222$ …… (1)

Since one decimal is given, so multiply both sides of equation 1 by 10.

That is $10x=-42.222$ …… (2)

Subtract equation 1 from equation 2,

then it is a rational number.

As it is rational number then it is a real number.

Therefore, the set of numbers to which $-4.\overline{2}$ belongs is:

Rational (Q) and Real (R).