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

1 Answer
Jun 26, 2015

Answer:

#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.