It is an integer, and hence it is a rational and real number as well.
This venn diagram from this site shows the different sets of numbers. You can see that if a number is part of a smaller set, then it is part of the larger sets around it.
- Whole numbers are the same as natural numbers. They are numbers like 1, 2, 3, which are used for counting. -2 is not one of these.
- Integers are numbers that do not have a fractional part. That is, if you were to write them as decimals, there would be nothing but 0 after the decimal. -2 is an integer.
- Rational numbers are numbers that can be expressed as a fraction. The number -2 can be expressed as ##-2/1## and so it is a rational number.
- Real algebraic numbers are those which are the zero (or root) of some polynomial function. -2 is a root of the function ##f(x) = x+2## and so is an algebraic number.
- Real numbers are those that do not have an imaginary component. The imaginary unit i is defined as the square root of negative one: ##i= sqrt(-1)##. Since -2 does not have that, it is real.