# Difference between Rational and Irrational Numbers | Rational vs. Irrational Numbers

## Rational vs. Irrational Numbers

Difference between Rational and Irrational: – In mathematics, numbers are nothing more than the representation of values ​​by means of symbols, words or figures. In general, they are used to define a particular quantity. They are also used to set measurements, label and sort things.

Numbers are infinite and can be categorized into various types according to certain characteristics; one of those categories is based on whether the numbers are rational or irrational.

## Difference between Rational and Irrational Numbers

If you have doubts about what is the difference between rational?
and irrational numbers or you are simply looking for a little more information to complement what you already know, then continue reading, because below we explain everything you want and you need to know about this interesting topic that probably have already left you homework in school.

Rational numbers
Rational numbers are known as those that can be expressed as a fraction, with a denominator and numerator other than zero. In other words, they are those that are expressed as the quotient of two nonzero integers.

In the same way, all decimals that are repeated fall into the category of rational numbers. Any rational number can be represented in a number line.

Examples: 8 (since it can be expressed as 8/1), the square root of 16 (which is 4 and can be expressed as 4/1) and 2.77777 (because as stated above, all decimals that are repeated are rational).

Irrational Numbers
On the other hand, irrational numbers are the opposite of rational numbers (as their name implies). That is, they cannot be expressed as a fraction with denominators other than zero. They can only be expressed as the quotient of two integers.

It is important to mention that many square, cubic roots … fall into the category of irrational numbers. However, as already seen in the previous case; not all roots are irrational numbers. These numbers can be expressed as non-terminal decimals and repetitive decimals.

Examples of irrational numbers would be: the number pi (3.14159265358 …), 4/0, many more. Finally, rational and irrational numbers tend to exert different functions. The former usually result when working with measures, while the latter occur more frequently when theoretical calculations and definitions are worked out.