##1/3## is a rational number being a number of the form ##p/q## where ##p## and ##q## are integers and ##q != 0##.
It is not a natural number whole number or integer.
Numbers can be classified as follows:
Natural numbers are the numbers ##0 1 2 3…## or ##1 2 3…##
Some people prefer to start at ##0## and others at ##1##.
Whole numbers are the numbers ##0 1 2 3…##
this is almost the same definition as natural numbers but does explicitly include ##0##.
Integers include negative numbers along with the previous ones so they are the numbers ##0 1 -1 2 -2 3 -3…##
Rational numbers are all numbers of the form ##p/q## where ##p## and ##q## are integers and ##q != 0##. Note that this includes positive and negative integers since if you let ##q=1## then ##p/q = p/1## can be any integer.
Real numbers are any numbers on the real line. This includes rational numbers but also includes numbers like ##sqrt(2)## and ##pi## which are not rational.
Irrational numbers are any numbers which are not rational.
Algebraic numbers are numbers which are roots of polynomials with integer coefficients. For example ##root(3)(2)## is algebraic because it is a root of ##x^3 – 2 = 0##. Every rational number is algebraic.
Transcendental numbers are numbers which are not algebraic. They include numbers like ##pi## and ##e##. In fact most real numbers are transcendental.