# What is the formula for finding rational numbers

## Rational numbers

Reading time: 5 min

The rational numbers become necessary when we divide whole numbers with one another, because the division can produce results that are no longer whole numbers. As an an example:

(is a fractional number)

Division of two whole numbers no longer results in a whole number. We write as a fraction. This number is no longer in the set of integers, we write:

Rational numbers are numbers that can be represented using fractions. The numerator and denominator are whole numbers.

This set of numbers has the sign (what for **Q**uotient, the result of a division).

In general, a rational number is a number of the form, where and must be integers. In addition, must not be so that no division by zero occurs. Generally:

What the formula means: (rational numbers) (are) the integers () and, and that (on condition that) is not.

Any whole number can be represented as a fraction. Therefore every integer is also a rational number.

The reason for this is that we can also write them as a fraction. For example: . This is known as a sham break.

The natural and whole numbers are considered a subset of the rational numbers, one writes \ (\ mathbb {N} \ subset \ mathbb {Z} \ subset \ mathbb {Q} \)

Examples of rational numbers:

There are infinitely many rational numbers in the direction of minus infinity (-∞) and in the direction of plus infinity (+ ∞).

In addition, there are infinitely many numbers between two rational numbers. Example: There are infinitely many more fractions between and.

Irrational numbers, for example, are not rational numbers. As an example of an irrational number, √2 or the circle number π (≈ 3.14159) can be mentioned.

### Features of rational numbers

The rational numbers have the following characteristics:

- They can be represented as a fraction (e.g. or or or)
- They have:

- no decimal places (example),

- finite number of decimal places (example) or

- infinite number of decimal places (example) - If the number has an infinite number of decimal places, these are periodic.

### Rational numbers in school

In school mathematics, one usually speaks of “rational numbers” when one introduces the calculation with negative whole numbers and also adds the fractions to the whole numbers. The handling of negative numbers is then particularly new for students. This can sometimes lead to misunderstandings.

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