Rational numbers are compared in a variety of ways, such as being placed on a number line or used with inequality symbols. Often, comparisons between rational numbers are simple relations that demonstrate which one is bigger and sometimes how much. Comparing rational numbers becomes more difficult if the numbers have complicated decimals or are written as fractions.
A rational number is any number that can be represented as a fraction in which both the numerator and the denominator are integers. Irrational numbers are often created by imperfect roots and terms like pi or the Euler number. Irrational numbers have non-repeating, non-terminating decimals.
If both numbers are integers, a comparison is usually straightforward. For example, if the rational numbers are 4 and 6, a relation that compares them could be written as 4 < 6. Similarly, on a number line that increases by one from left to right, 6 would be placed two spaces to the right of 4.
If the numbers are written as improper fractions, they can be more difficult to interpret until they are rewritten as mixed numbers or decimals. For example, a problem might ask for a comparison of 17/4 and 21/9. Once taken out of their fractional form, these numbers can be written as 4.25 and approximately 2.33 respectively. Because 4.25 > 2.33, 17/4 > 21/9.