**Rational number:**

A number which can be written in the form a/b where *a* and b are integers and *b* ≠ 0 is called a rational number. Rational numbers are of two types depending on whether their decimal form is terminating or recurring.

**Irrational number:**

A number which cannot be written in the form a/b, where *a* and *b* are integers and b ≠ 0 is called a irrational number. Irrational numbers which have non-terminating and non-repeating decimal representation.

The sum or difference of a two irrational numbers is also rational or an irrational number.

The sum or difference of a rational and an irrational number is also an irrational number.

Product of a rational and an irrational number is also an irrational number.

Product of a two irrational numbers is also rational or an irrational number.

**Theorem:**

Let p be a prime number. If p divides a^{2}, then p divides a, where a is a positive integer.

**Theorem:**

If p/q is a rational number, such that the prime factorisation of q is of the form 2^{a}5^{b}, where a and b are positive integers, then the decimal expansion of the rational number p/q terminates.

**Theorem: **

If a rational number is a terminating decimal, it can be written in the form p/q , where p and q are co-prime and the prime factorisation of q is of the form 2^{a}5^{b}, where a and b are positive integers.

**Theorem: **

If p/q is a rational number such that the prime factorisation of q is not of the form 2^{a}5^{b} where a and b are positive integers, then the decimal expansion of the rational number p/q does not terminate and is recurring.