##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.