What is a rational number?

Numbers that are fractions, whole numbers and the decimals, are called as Rational numbers. These numbers are used by us in in our day to day life. You can write these numbers as two integers ratio. Irrational numbers contrasted the rationale numbers, such as cosines, sines etc. If we go by the definition then a number becomes a rational number if it can written in the a/b form ensuring that a as well as b stands as the integers, and that value of b isn’t the zero. It is clear and understood that all the fractions are in the same form, hence making all the fractions the rational numbers.

Let’s get into the detail of the terminology of rational  numbers. Term rational in mathematics is used in the form of noun, which abbreviates the rational number. Adjective rationals expresses that coefficients sometimes are the rational numbers. Say, to quote an example, rational point is the point that has the rational coordinates. This is the point, where it’s coordinates are the rational numbers. Matrix of the rational numbers is termed as rational matrix. When it comes to rational polynomial then polynomial may be with the rational polynomial that have rational coeeficients. Though preferences is given to the term polynomial when compared with rationals, so that confusion is avoided when it comes to rational function and rational expressions.

What is the difference between Rational Numbers and Irrational Numbers

So, it is the proven fact that mathematics is all about numbers and numbers represent the mathematics. As we discussed above that rational numbers are the ones that are fractions and integers, on the other hand irrational numbers are the ones who cannot be expressed in fractions.

Key differences between the two are listed below:

  1. You can write rational numbers in the ratio of 2 integers whereas irrational numbers cannot be defined in two integers ratio.
  2. Denominator and numerator in rational numbers are the whole numbers, and the denominator will never equal to zero. Whereas, it is not possible to write irrational numbers in fraction.
  3. Numbers with the perfect squares are included in rational numbers, such as 25, 16, 9 etc. While surds such as 5, 7, 11 are included in irrational numbers.
  4. Decimals which are repeating and finite are included in rational numbers. Opposite to this, numbers which have infinite and non-repetitive decimal expansion are included in irrational numbers.

Examples of Rational and Irrational Numbers

Let’s have a look on few examples of both rational and irrational numbers:

Rational Numbers

  1. 5
  2. 1
  3. 0
  4. √4 – rational

Irrational Numbers

  1. √2 – irrational
  2. √5 – irrational

What Conclusion is derived from this article

With the points that have been discussed here, there is no doubt that rational expressions can be expressed in decimal form as well as in fraction form. On the other hand irrational numbers are expressed only in the form of decimal and not in the fraction form. All the integers are represented as rational numbers but not all the irrational numbers are non-integers.