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# List of Rational Numbers

TopRational numbers is a big subset of real number set which are not irrational. These are the numbers that can be represented in the form of $\frac{\text{Numerator}}{\text{Denominator}}$, such that both numerator and denominator are integers and the denominator of the fraction is not equivalent to zero. The list mentioned below is the list of rational numbers and their types.

Natural Numbers: The counting numbers that begin from 1 are called natural numbers. Example: 1, 2, 3, 4 …, $\infty$

Whole Numbers: Natural numbers including zero are whole numbers. Example: 0, 1, 2, 3, 4 …, $\infty$

Integers: The whole set of Positive and Negative Numbers, such that that positive numbers are Natural Numbers and negative ones are their negation including zero are integers. Example: - $\infty$, … - 4, - 3, - 2, - 2, 0, 1, 2, 3, 4 … $\infty$. There are two types of integers, notable integers and named integers.

Cardinal Numbers: These are the rational numbers that are used to evaluate the size of a set. These are strictly natural numbers.

Powers of Ten: The rational numbers represented in the scientific notation, such as 1.2 x 1012 are called powers of ten.

Highly Composite Numbers: These are the positive integers with more divisors, than any positive Integer smaller than they are. Example: 1, 2, 4, 6, 12 etc.

Fractional Numbers: The rational numbers in $\frac{a}{b}$ form are the fractional numbers. Example: $\frac{1}{3}, \frac{13}{15}$, etc.

Prime Numbers: The numbers that have two divisors, 1 and the numbers themselves. Examples: 2, 3, 5, 7, 11, etc.

Perfect Numbers: Numbers that can be obtained by summing up all their proper divisors. Example: 6, 28, 496, etc.

This is a wide-ranging list of rational numbers. The classification is helpful in various computations. Let us perform some calculations on the rational numbers.

One of the important properties of rational numbers is that we can list endless number of rational numbers between two given rational numbers.

Let us see an example on how we can do that.

Example: What is the list of rational numbers between 2 and 3?

Solution: We can write 2 as 2.0. Now, if we increment the decimal digit by one, we will get the list as 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8 and 2.9. Notice that all the above mentioned numbers are more than one and less than three. As such, they lie between 2 and 3. Furthermore, if we pick up a certain number from the list, say 2.1, write it as 2.10 and then increment the tens unit of decimal digits by one, we will again generate a new list of numbers that will lie between 2 and 3. It will be 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18 and 2.19. So, as it is clear, the list of rational numbers between 2 and 3 is 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8 and 2.9, … , 2.11, 2.12, 2.13, 2.14, 2.15, 2.16, 2.17, 2.18 and 2.19, ... and so on.

List of rational numbers is shown below:

 $\frac{1}{1}$ $\frac{1}{2}$ $\frac{1}{3}$ $\frac{1}{4}$ $\frac{1}{5}$ $\frac{1}{6}$ $\frac{1}{7}$ $\frac{1}{8}$ $\frac{1}{9}$ $\frac{2}{1}$ $\frac{2}{2}$ $\frac{2}{3}$ $\frac{2}{4}$ $\frac{2}{5}$ $\frac{2}{6}$ $\frac{2}{7}$ $\frac{2}{8}$ $\frac{2}{9}$ $\frac{3}{1}$ $\frac{3}{2}$ $\frac{3}{3}$ $\frac{3}{4}$ $\frac{3}{5}$ $\frac{3}{6}$ $\frac{3}{7}$ $\frac{3}{8}$ $\frac{3}{9}$ $\frac{4}{1}$ $\frac{4}{2}$ $\frac{4}{3}$ $\frac{4}{4}$ $\frac{4}{5}$ $\frac{4}{6}$ $\frac{4}{7}$ $\frac{4}{8}$ $\frac{4}{9}$ $\frac{5}{1}$ $\frac{5}{2}$ $\frac{5}{3}$ $\frac{5}{4}$ $\frac{5}{5}$ $\frac{5}{6}$ $\frac{5}{7}$ $\frac{5}{8}$ $\frac{5}{9}$ $\frac{6}{1}$ $\frac{6}{2}$ $\frac{6}{3}$ $\frac{6}{4}$ $\frac{6}{5}$ $\frac{6}{6}$ $\frac{6}{7}$ $\frac{6}{8}$ $\frac{6}{9}$ $\frac{7}{1}$ $\frac{7}{2}$ $\frac{7}{3}$ $\frac{7}{4}$ $\frac{7}{5}$ $\frac{7}{6}$ $\frac{7}{7}$ $\frac{7}{8}$ $\frac{7}{9}$ $\frac{8}{1}$ $\frac{8}{2}$ $\frac{8}{3}$ $\frac{8}{4}$ $\frac{8}{5}$ $\frac{8}{6}$ $\frac{8}{7}$ $\frac{8}{8}$ $\frac{8}{9}$ $\frac{9}{1}$ $\frac{9}{2}$ $\frac{9}{3}$ $\frac{9}{4}$ $\frac{9}{5}$ $\frac{9}{6}$ $\frac{9}{7}$ $\frac{9}{8}$ $\frac{9}{9}$