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How to check given number is rational or irrational by looking at its decimal extension

Inderjeet Singh

20/01/2020 0 0

- Rational, The decimal expansion of rational number, either stops or repeat infinitely many times
- Irrational, The decimal expansion of irrational number, neither stops nor repeat.
Examples
- 7.65 it is a rational number because decimal expansion stops
- 4.346346346346346........ it is a rational number because decimal expansion repeats several times. However not stops
- 1.101001000100001.... it is an irrational number because it's decimal expansion neither stops nor repeat.
- 5.76438483728580193201.... it is again irrational number decimals expansion non-stop and no repeat.

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How to check given number is rational or irrational by looking at its decimal extension

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