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A number is an irrational if and only if its decimal representation is

A number is an irrational if and only if its decimal representation is

Question : A number is irrational if and only if its decimal representation is :

  1. Non-terminating
  2. Non-terminating and repeating
  3. Non-terminating and non-repeating
  4. Terminating
Solution :
The correct option is 3. non-terminating and non-repeating
According to the definition of an irrational number, If written in decimal notation,
an irrational number would have an infinite number of digits to the right
of the decimal point, without repetition.
Hence, a number having non terminating and non-repeating decimal
representation is an irrational number.
So, option 3. is correct.

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