Difference Between Real Number and Rational Number

The mathematics are very useful and interesting, but often create confusion in people to the point that some fear them and avoid them . At school they regularly talk to us about numbers, but sometimes we don’t understand that there are different types of them. Difference Between Real Number and Rational Number

On this occasion we will tell you what is the difference between them, since it is a fact that you should not forget.

REAL NUMBERS  Difference Between Real Number and Rational Number

Real numbers include both rational and irrational numbers. The real number system can be divided into many subsets.

A real number refers to any number that can be found on a number line. The number line can be defined as a geometric line where an origin point is drawn. The p daubs found on the right side of the origin are considered as positive numbers, while numbers on the left side of the origin are considered negative . The infinite does not fall into the real number category. The root of -1 is not a real number, therefore it is considered an imaginary number.


A rational number is a number that is determined by a relation that is defined as (p / q), where p represents some integer and q a natural number other than zero.

These numbers are a subset of the real numbers. On the other hand, real numbers that cannot be expressed as the quotient of two integers are called irrational numbers. 

Key differences between rational number and real number

  • Real numbers can be rational or irrational and can take any value expressed on a number line; while rational numbers are those that can be expressed as a fraction, but with a denominator other than zero.
  • Real numbers include (but are not limited to): positive, black, integer, rational numbers, square roots, cube roots.
  • Rational numbers include: 3/4 as a fraction form. Square root of 16, which would be 4 and could be expressed as 4/1. Decimal repetitions are rational, example: 0.777777.

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