Is -3 a rational, irrational, natural, whole, integer or real number?

1 Answer
Jul 1, 2015

Answer:

#-3# is an integer (and thus also rational and real)

Explanation:

natural or whole numbers (the terms are generally considered synonymous) are non-negative "counting numbers". Occasionally they are denoted by the symbol #NN#. There are some differences in definitions which sometimes include #0# and sometimes exclude #0# from #NN#.

#-3# is negative so it is not a natural or whole number.

integers are natural numbers extended to include negative versions of all the natural numbers (and #0# if it were excluded by the "natural number definition"). The normal symbol for integers is #ZZ#

#-3# obviously falls in this category.

Rational numbers are numbers that can be expressed as a fraction or ratio of two integers. Rational numbers are denoted #QQ#.

Since #-3# can be written as #(-3)/1#, it could be argued that #-3# is also a real number.

Irrational numbers are numbers that can not be expressed as a ratio (or fraction) of two integers but could represent a linear distance.

Real numbers are a union of both rational and irrational numbers