Question

Is `1/3` a rational, irrational number, natural, whole or integer?

Answer 1

`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.

Explanation:

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.