Decimal expansion of rational numbers
Every rational number can be expressed as a terminating decimal or non terminating but repeating decimals.
1. Terminating Decimal
- The remainder becomes zero
The word “Terminate” means “end”. A decimal that end is a Terminate.
i.e, A terminating decimal doesn’t keep going a terminating decimal will have finite number of decimal after the decimal point.
2/5 = 0.4, 3/8 = 0.375, 20/16 = 1.25
2. Non Terminating and Repeating (Recurring decimal)
- The remainder never becomes zero
A decimal in which a digit or a set of finite number of digits repeats periodically is called non repeating (recurring) decimals.
1/3 = 0.33333333333333…………… = 0.3‾