**The name ""rational numbers""** comes from the Latin word ratio that in translation means ""relation"". Let's consider in more detail what numbers are.

By definition by rational is called number it number which can be presented in the form of a common fraction. The integer, and a denominator - natural has to be numerator of such fraction. In turn natural numbers are those which are used at the account of objects, and whole - all this natural, opposite to them and zero. A set of rational numbers call a set of representations of these fractions. The fraction should be understood as result of division, for example, fractions 1/2 and 2/4 should be understood as a similar rational number. Therefore fractions which can be reduced bear one mathematical sense from this point of view. The set of all integers is a subset rational. Let's consider the main properties. Rational numbers have four main properties of arithmetics, namely - multiplication, addition, subtraction and division (except zero) and also an opportunity to order these numbers. For each element from a set of rational numbers the existence of the return and opposite element, existence of zero and unit is proved. The set of these numbers is associative and is commutative both on addition, and on multiplication. Among properties there is the known theorem of Archimedes which says that whatever took a rational number, it is possible to take so many units that the sum of these units will surpass this rational number. Let's notice that the set of rational numbers is the field. The scope of rational numbers is very wide. These are those numbers which are applied in physics, economy, chemistry and other sciences. **Rational numbers** play great value in financial and banking systems. At all power of a set of rational numbers, it is not enough for the solution of problems of planimetry. If to take nebezizvestny Pythagorean theorem, there is an example of irrational number. Therefore there was a need to expand this set to a set of so-called real numbers. Initially the concepts ""rational"", ""irrational"" belonged not to numbers, and to commensurable and incommensurable sizes which were called sometimes vyrazimy and inexpressible.