Is 0. natural number, whole number, integer, rational number, irrational number

A natural number is a single digit whole number, a whole number is any number without a decimal or fraction including zero, an integer is any whole number and their opposites, a rational number is any number that can written as a fraction of two integers(a/b where b can't equal 0), and an irrational number is a number that cannot be expressed in a fraction of two integers. So terminating decimals are rational while repeating decimals are irrational.