Rational Numbers
The rational numbers are those numbers which can be expressed as a ratio between two integers. For example, the fractions 1/3 and -1111/8 are both rational numbers. All the integers are included in the rational numbers, since any integer z can be written as the ratio z/1.
Numbers which cannot be written as a ratio of integers are called irrational.
All decimals which terminate are rational numbers (since 8.27 can be written as 827/1000.) Decimals which have a repeating pattern after some point are also rationals: for example,
0.083333333... = 1/12.
The set of rational numbers is sometimes written Q for short. It is closed under all four basic operations: that is, given any two rational numbers, their sum, difference, product, and quotient is also a rational number (as long as we don't divide by 0.)
The Venn diagram below shows the relationships of the various sets of numbers.
