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‾

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