A number is called a rational number if it can be written in the form of p/q where p and q are integers and q≠0.
A number is said to be irrational if it cannot be written in the form p/q where p and q are integers and q≠0.
TYPES OF DECIMALS
- Terminating: The decimal expansion terminates after a finite number of steps.
- Non-terminating recurring: The decimal expansion does not terminate but the numbers keep repeating.
- Non-terminating non-recurring: The decimal expansion neither terminates nor has a repeating value.
The decimal expansion of a rational number is either terminating or non-terminating recurring.
The decimal expansion of an irrational number is non-terminating and non-recurring.
The collection of rational and irrational numbers makes up the real numbers.
IDENTITIES FOR REAL NUMBERS: