What is a Rational numbers

Rational numbers

Rational numbers are numbers that can be expressed by dividing one integer by another nonzero integer. Thus all rational numbers take the form of fractions or quotients. These are written as one number, the numerator, divided by a second, the denominator.

When expressed in decimal form, rational numbers either come to an end after a finite number of digits, or one or a number of digits are repeated forever. For instance, 0.3333333... is a rational number expressed in decimal form. In fraction form, the same number is 1/3. It is also true to say that any decimal number that comes to an end or repeats must be a rational number, expressible in fractional form.

Since there is an infinite number of integers, it is not surprising to find that there are an infinite number of ways of dividing one by another, but this does not mean there is a “greater infinity” of rational numbers than that of the integers.