# What is the rational numbers

Name "rational numbers" It comes from the Latin word ratio, which means "attitude". Let's take a closer look at that kind of number.

By definition, a rational number is called the number that can be represented in the form of a common fraction. The numerator of such a fraction has to be an integer, and the denominator - natural. In turn, the natural numbers - the ones that are used in counting objects, but whole - it is all natural, and opposing them nol.Mnozhestvom rational numbers is called the set of representations of fractions. The shot should be understood as the result of the division, such as 1/2 and 2/4 fractions to be understood as analogous to a rational number. Therefore, the fraction that can be reduced are a mathematical sense, from this point of view. The set of all integers is a subset of the rational. Consider the basic properties. Rational numbers have four basic properties of arithmetic, namely - multiplication, addition, subtraction and division (other than zero), as well as the ability to organize these numbers. For each element of the set of rational numbers proved the presence of the reverse and the opposite element, the presence of zero and one. Many of these numbers is associative and commutative as the under addition and under multiplication. Among the features there are well-known theorem of Archimedes, which states that whatever took rational number, you can take as many units, the sum of these units exceeds a given rational number. Note that the set of rational numbers is a field. Scope of rational numbers is very wide. These are the numbers that are used in physics, economics, chemistry and other sciences. Great value rational numbers play in the financial and banking system. With all the power of the set of rational numbers, it is not enough to solve the problems of plane geometry. If you take nebezizvestny Pythagorean theorem, there occurs an example of irrational numbers. Therefore, it became necessary to expand this set to a set of so-called real numbers. Initially, the concept of "rational". "irrational" referred not to the numbers, and to comparable and incommensurable values, which are sometimes called expressible and inexpressible.