A number is called a rational number if it can be written in the form a/b where a and b are integers and b ≠ 0.

A number is called an irrational number if it cannot be written in the form a/b,
where a and b are integers and b ≠ 0.

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

Rational numbers are of two types depending on whether their decimal form is terminating or recurring.

Theorem: If p/q is a rational number, such that the prime factorisation of q is of the form 2^a5^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^a5^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^a5^b where a and b are positive integers, then the decimal expansion of the rational number p/q does not terminate and is recurring