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A number which can be expressed in the form *p*/*q*, q ≠ 0 where *p* and *q* are integers, is called a rational number. All integers and the numbers like *etc.,* are rational numbers. Rational numbers can also be represented as terminating decimals like or by non-terminating but repeating decimals like

The non-terminating and non-repeating decimals always represent irrational numbers.

Let us now investigate the form of the integer *q* in the rational number *p*/*q*, which decides whether the decimal representation of *p*/*q *is terminating or non-terminating and recurring. This investigation starts with the division lemma named after famous Greek Mathematician Euclid who discovered this important result.

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