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Rational numbers can be expanded in the form of decimals by doing the usual long division.
A terminating decimal is a decimal number that has the finite number of digits the decimal point.
A recurring decimal is a decimal number that has repeating number/numbers which continuous infinitely.
Now we will analyse the decimal expansions of different types of rational numbers.
Rational number | Value with the help of long division | Nature of the decimal expansion |
Terminating decimals | ||
Terminating decimals | ||
Recurring and non-terminating decimals | ||
Recurring and non-terminating decimals |
In the above examples, examples \(1\) and \(2\) gives terminating quotients, and the examples \(3\) and \(4\) gives the recurring decimals quotients.
Thus, it can be concluded as follows:
A rational number can have either a terminating decimal expansion or a non-terminating recurring decimal expansion.