What is the difference between real numbers and rational numbers?

Question

Gianna Caruso · Accepted Answer

Although all rational numbers are real numbers, there are some numbers (irrational numbers) which are not rational numbers.

Any number that can be expressed as a ratio between two integers with a non-zero denominator is considered rational. The numbers that fit on a real number line are called real numbers. While every rational number can be represented on a real number line, some non-rational numbers can also be represented on such a line. Numbers like #sqrt2#, #sqrtx# (where #x# is a positive rational number but not the square of a rational number), #pi# etc. cannot be expressed as ratio of two integers like rational numbers, but can be represented on real number line. These numbers are called irrational numbers. Therefore, even though all rational numbers are real numbers, some numbers—known as irrational numbers—are not rational.

Genesis Amaya · Answer

undefined Real numbers include all rational and irrational numbers. Rational numbers can be expressed as the quotient or fraction of two integers, where the denominator is not zero. In contrast, irrational numbers cannot be expressed as fractions and have non-repeating, non-terminating decimal representations. Therefore, while all rational numbers are real, not all real numbers are rational.