A rational number is one that can be expressed in the form
a/b, if a and b are two integers.
When expressed in the
decimal form a rational number either has a finite number of decimal digits, for example
2.5 or 2.1625, or after a finite number of decimal digits, the set of decimal digits
repeats itself. For example, the number 3.3333... is a rational number as the decimal
digit 3 is one that repeats, this can be written as 10/3. Similarly in the rational
number formed by 25/7, the decimal notation is 3.571428571..., here the set of digits
571428 repeat in the decimal digits.
Irrational numbers on
the other hand cannot be expressed as a/b, where a and b are integers. Examples of
irrational numbers are pi, e, sqrt 3, sqrt 7, etc. When an irrational number is written
in the decimal notation, the decimal digits do not form sets that are repetitive. For
example, pi = 3.141592654... It is not possible to find a group of digits that repeat
even if an infinite number of them are taken.
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