A rational number is a number that can be written as a fraction of integers.

Integers are whole numbers and their negatives: \(\dots,-3,-2,-1,0,1,2,3,\dots\).

The word "rational" comes from the word "ratio" as we can think of ratios as fractions.

All real numbers are either rational numbers or irrational numbers (numbers that can't be written as fractions).

Another way of thinking of rational numbers is that they are the numbers that can either be written as terminating decimals (numbers for which the decimal places end) or repeating decimals (numbers for which the same few decimal place digits are repeated over and over again).

Some examples of rational numbers are:

• \(\dfrac{1}{4}\) is a rational number (\(1\) and \(4\) are integers).
• \(0.35\) is a rational number. It can be written as \(\dfrac{35}{100} = \dfrac{7}{20}\).
• \(0\) is a rational number. It's equal to \(\dfrac{0}{1}\), or zero over any non-zero integer you like.
• \(5\) is a rational number. It's equal to \(\dfrac{5}{1}\).
• \(-3.14\) is a rational number. It's equal to \(\dfrac{-314}{100}\).

However, \(\pi\) and \(\sqrt{2}\) are irrational numbers. When you write them as decimals, the digits go on forever and ever, without any repeating pattern: \(\sqrt{2} = 1.4142135623\dots\)